"German engineering is the world's finest!"

It is even today difficult to cushion the head and next against shock, so a hammer or likewise forceful blow to the head has always been a pretty effective strategy in general, but a severe impact to the chest can stop the heart, colapse lungs, crush ribs, or cause internal hemorrhaging. The armor might prevent you from being directly harmed but it still transmits force, just because you have your arm in a metal box doesn’t mean that if I hit that box with a sledge hammer your bones won’t break, if it were that simple we wouldn’t have to worry about car accidents or such so much would we? Much of modern crash safety involves absorbing force, not in the metal of the car not deforming. Modern armor is much the same- ablative armors and reactive artists that are more effective because they deform to dissipate energy that would otherwise harm the systems or crew of a vehicle for example. .

So I mean- they are cool swords and we also have to remember that the tools of war are a system- the terrain and materials and logistics and circumstances of a time and place dictate effectiveness. It isn’t so much that one weapon is generally better than another in most cases so much as for a given time or place one weapon may offer advantage. One can argue a firearm is universally better than a sword- but this isn’t inherently true. If you lack the facilities and technologies to maintain the firearm and keep it supplied with ammunition, it becomes generally fairly useless as a tool of war quickly. When we take weapons out of their time and place they lose context- was it common for foot soldiers to need to fight mounted troops such as peasants vs. An elite class? Then certain weapons specialized for fighting mounted infantry from the ground might be superior to another weapon. From 2 feet away seated a dagger likely beats a bow or a sword. Context is key.

Versus modern steel, I wonder how well a simple steel water pipe from Lowes would shake out.

Lol. That’s actually a sort of complicated answer- but as an overall generality most modern steel used for most things like that is going to be “better” than the steel used in swords around the medieval period. Even cheap modern steels tend to be much purer and more consistent than what they had to work with. Our ability to select and tailor alloys is much more advanced as well.
Your average Lowe’s style steel water pipe is probably a 304 or 316 stainless. These relatively soft alloys aren’t the best for making sharp knives but they do have some uses in knife making. As a pipe they are going to likely fare pretty well against a sword overall, the caveats being some things like wall thickness and overall size. Because the sword is generally solid and the pipe is not, the comparison comes down to dimensions since using the same amount of steel in both, the pipes overall strength will come down to dimensions.

We could try to even it out by saying two identical pipes made of modern pipe steel and period sword steel or two swords of the same- but that still is a touch imperfect as sword steels and pipe steels are often selected for different properties. A bit like comparing the strength of glass to polycarbonate type plastic- glass is generally harder but poly will generally be tougher. “Bullet proof glass” is usually a plastic, but we need a certain thickness. The same is true in a structural application where glass can sometimes be used as a structural member at a thickness that most clear plastics don’t perform as well or at all.
But in modern times on a metallurgical level most steels that aren’t just- the cheapest pot metal junk steel- are “better.” That said there are examples of antique steel that could stand up very well against many modern steels, the ability to produce such steels wasn’t wide spread and it generally was consistently achievable. The consistency in strength and…

.. purity is magnitudes superior with modern steels on average. Meaning that if you had 100 swords made in the period that there were good odds that some were likely to fail and a few were likely to be much better blades than the others. Higher end blades were often tested before delivery, the higher end the blade the more it was tested, with modern blades and steel tools there is generally little or no need to test each product as it can be reasonably safely assumed that there will be a few duds but the vast majority of product is going to be faulty uniform to a single sample off the batch, and where critical we have technology to spot imperfections in metals etc. so below a critical “aerospace” type tolerance, our metallurgy and manufacturing are generally high enough that simple “every day use” items are pretty darn good.

Tl:dr- the pipe probably wins overall, but there are some exceptions and some antique steel was high quality, it just took them a lot more care and effort, or a healthy dose of luck, to produce steel items approaching a general modern quality. Overall the highest quality metals and goods we can produce are beyond the capabilities of medieval metal working based on what evidence we have, or what we can mass produce quickly would represent a significant investment to produce a single item of comprable form and function.

The katana was an effective weapon, but not quite a legendary physics defying super weapon and as you say (or I say in my other posts) it was essentially made from pig iron due to poor ore quality in the region and lack of technology in alloys. A superior metallurgical quality blade can be made in the same form relatively “simpler” with high quality allow steels. Asides cultural and historical importance the primary reason for prizing and for the modern production of the “traditional” katana come primarily from its artistic merits as a small production hand made work of art. The numerous processes involved in crafting the sword create distinct aesthetics like patterning on the blade which most mass produced blades attempt to mimic using machining or chemical means after the blade is formed as opposed to being an intrinsic mark of the creation process and intensively don’t by hand to create what is essentially a unique “finger print” to each hand made blade. These mass produced..

.. markings generally lack the complexity of the hand made ones and generally except for the highest end attempts at “faking” the look of a traditional blade can easily be identified as “fake” decoration.
With that said we also have to remember that the sword in general is romanticized in the modern day. It is complex and I won’t get into the entire thing, but across most places and times the sword was… not generally the most effective weapon on most battlefields. Often times it served more ad a last resort- similar to how many militaries equipped or still equip certain troops with side arms like hand guns even though they have rifles or long arms. Bows and other ranged weapons tend to be historically favored as the first choice of engagement where their use was practical. It makes sense. Hit the enemy from where they can’t hit you! Then pole arms- spears and such long weapons. Such weapons use the same principle of ideally keeping enemies further from your body and thus being..

.. able to harm you. Their reach gives som measure of protection against multiple foes “ganging up” as you can theoretically cover a large area with danger to those entering. Pole arms are generally more useful by and against mounted troops (like those on horses) since they have the reach to more easily cover the distance from ground level to horse level or the distance between two horses. They often used wooden shafts, wood generally being a cheap and plentiful material and one which if properly selected is strong, hard, and not terribly failure prone. A pole arm can be as simple as a long sharpened wood stick meaning less cost and resources in metals which were often expensive or limited historically. A pile arm with a metal end still generally uses less metal than a sword and the end is generally simpler to make than a sword. The end of the pole arm generally isn’t used or at much risk for “blade to blade” combat or such so you can use metal and designs that are less practical in..

.. a sword. And if the pole arm is damaged, you can generally replace the wooden shaft and reuse the metal tip.
Behind pole arms for closer quarters in combat tended to be clubs and axes and maces and such. Like the pole arm these weapons generally required no metal or less metal than a sword, they were generally simpler to make and cheaper to buy.
Swords in generally are not very effective against armor, of almost any sort. Clubs and axes and war hammers and such generally were more effective against armor, especially hard armors like metal plates or chain mails.
They were capable of more readily causing blunt trauma or knock back against armored enemies. The relatively light weight of a sword and the surface area of its strike reduce the force from a blow that is focussed into the armor wearers body. Even larger,
Generally less brittle, European swords would be damaged by metal on metal contact and hitting armor, especially metal armor, quickly wears at a sword.

So the repeated blows to an armored foe, if one could land enough to wear at the armor or wearer without being themselves neutralized, would almost certainly all but ruin most swords.
So really, swords were good for closer range combat, primarily against unarmored opponents (though a skilled fighter could find gaps in armor etc. to penetrate), and were generally expensive and not useful outside of combat. Many other weapons did have uses, bows for hunting, and many arms and such were farming implements or could be used as tools in other ways.
You seldom historically see many “average” people owning swords because they generally were expensive and not very useful outside of battle, and in battle the weapon tended to be less suited for large force melee skirmishes and more suited for individualized combat.

Of course in later periods swords did become or common as back up or even primary weapons in some armies. Swords have a portability that may pole arms do not. While it is somewhat inconvenient, one car carry a sword on their side and go about daily business but have a weapon ready when needed. This has value outside of the battlefield but where dangers may exist- much as police ay carry a pistol or club or such on them at most times even when in areas that are generally not war zones or crime dens- but they often have rifles or other weapons available but not on their person for dealing with situations other than a sudden need to enforce law or defend themselves.

While portable the sword in general isn’t great in tight spaces. Not enough room to swing it around, easy to get it caught up in walls or such. Many European swords were designed so that you could hold the lower part of the blade like a handle. This area wasn’t actually a blade as the cutting edge was usually further up. This allowed the sword to be used as a club or to disarm or to make it effectively shorter, for close spaces.
In general however, daggers and knives tended to be favored for such things. Daggers and knives follow the same principles above. Generally cheaper, simpler, easier to make, less metal than swords. They are lighter, easier to carry, easier to conceal. Daggers and knives also can be much more useful in daily life, they could be used as eating utensils, for various tasks like cutting rope or even for hobbies like whittling wood. In Japan various types of dagger and short sword existed, and these were often carried by various persons including samurai and

nobility. So swords as a whole are more complex and I can’t just say: “swords kinda suck…” or anything like that, but I just want to be clear that it isn’t that katana suck or anything like that- they just generally aren’t magical. The basic principles of tactics tend to favor certain things. As a general rule, for whatever field combat will occur in tactics favors the longest ranged weapon that is practical to those circumstances. A sword may be favored to a dagger for a one on one fight in living room, a dagger is favored perhaps to a letter opener in a one on one in a bathroom stall, and from across an open football field a bow is generally favored to a pike.
Katana like any weapon have their quirks- but they did make sense under certain circumstances and I can’t stress how clever the design is.