Avengers 4

As has been shown before in the marvel universe time travel doesn't effect the person traveling. So if he went back in time to kill thanos before he existed strange wouldn't be directly at risk of a paradox. Also as I said the wizards have had the stone long before thanos was even a thing. They've had it since they existed as an organization.

Since we don’t actually know when the earth wizards were formed, or when they got the stone, or when Thanos was born- we can’t really argue about who did what first. We can’t really speculate on the nature of MCU time travel much either. The “loop” scene from doctor strange- I could write a looong exposition on that. We don’t know that there is one time, or if the mechanism used is divergent timelines (although X-men movies have set up divergent timelines, if we include those.) we can’t say the traveler is completely uneffected, dr strange was killed, went back in time as alive, and then after returning to the “present” was alive despite having changed events that killed him. The “present” at the time of his travel he was dead- so his actions in the past are capable of effecting himself or he’d be dead- since he effectively changed events to save his life along with everyone else’s. The rules aren’t hard rules- narrative convenience.

He wasn't in control of the time stone anymore. He set it to loop and let go of the controls. He wasn't the traveler anymore the eye was.

Ignoring the technicalities of going back and killing Thanos, remember he has already wiped out half of the population of many many planets. Without him those people would have lived and it's possible that rather than one Thanos we'd have multiple people with similar ideals and enough power to cause more damage... Thanos was obsessed but he retreated once he'd accomplished his goal. In his way he wanted peace. Perhaps from those he left alive the tyrants would be worse than Thanos himself

That’s a big throat of my point. Of all the conjecture we can make from our vantage- Doctor Strange is one of the few characters who would actually know- and if it was at all a viable solution, I’d have to imagine he would have mentioned or tried it. We have to assume that it either isn’t possible, or is worse than not doing it.

... well.... or Dr. Strange is incompetent.

Wong straight up tells Dr. Strange to cut the shit BECAUSE it does affect him. He doesn't notice it, but it does. Agamotto lived before Thanos, but Thanos is thousands of years old and knows of the mantle of the Sorcerer Supreme. Creating a grandfather paradox out of it, while interesting, really doesn't make sense.