You can't mess with time. Even saving Buckbeak was a huge risk. And that was only a couple of hours previous. Imagine messing with 15-16 years and drastically changing a humans life.
In harry potter they dont actually CHANGE anything in time you idiot. Everything they do in the past already happened in the present. Think about the freaking dementor scene. He was saved, then he saved himself. It already happened. If he tried to save his parents they would end up dying anyways. You cant change what has already happened in the present. Learn your Harry Potter before you make stupid shit like this.
They knew exactly when buckbeak was about to die so they could o back and stop the killing (which never happened), with Harry's parents they are already dead and can't change that
All the time turners were destroyed in the 5th book. There would have been now way to use it during the battle of Hogwarts.