Except as we see in “The Prisoner of Azkaban” you can’t actually change the past with the Time Twister. All the things you do in the past have already happened. Yes, you can go back and free Buckbeak, but only because you already freed him, if you’d paid more attention you would have known it already. The timeline is always self-consistent, all time loops are stable.
If you go back in time to warn yourself you’ll always fail unless you already got the warning from your future self. If you go back in time to kill Tom Riddle you’ll fail, and likely find that your attempted meddling is what turned Hitler evil in the first place. The reason you know you’ll fail in your attempt to kill Hitler as a child is that you can read a history book and see that Hitler wasn’t killed as a child. It already didn’t happen.
Maybe you don’t like this version of time travel, but it’s perfectly reasonable and is the basis for lots and lots of time travel stories.
Here’s one for Voldemort: I have a collection of 7 objects that, quite literally, contain portions of my soul. What am I going to do to keep them safe? Why, I’m going to arrange to leave half of them in abandoned locations where any wizard or witch might conceivably stumble on them. The other half will belong to random people who have no clue as to the object’s significance, and who might do who-knows-what with it?
Sheese. The snake was the only horcrux he took reasonably good care of.
I sometimes wonder if there aren’t multiple writers. Some chapters - especially early ones - read like someone adapted a classroom lecture to the dialogue of fictional characters. Heck, the first chapters are even named after the logic lesson you’re supposed to learn. There are other chapters, though, that read like an actual story. Those chapters are more common later on.
I read through everything that’s up so far, but mostly because it was there. You’re right about criticism I’d have of it.
In A Very Potter Sequel, the second of the musical Harry Potter parodies staged at the University of Michigan, the plot involves Lucias Malfoy using a Time Turner to go back to Harry Potter’s first year at Hogwarts, intending to kill him before he can start interfering with Lord Voldemort’s return. Another character (it’s a bit of a spoiler to say who) also travels back in time to try to foil Malfoy’s plans.
Towards the end of the show (Act 2, Scene 13) one of the non-time traveling characters asks the time traveler “How was our first year at Hogwarts really supposed to go?” The time traveler replies “Well, looking back on it, it was actually supposed to go exactly like this. It just makes a lot more sense to me now.”
There should be a time travel story where the hero invents a time machine, reasons through the argument above to reach the conclusion that he shouldn’t travel back to kill Hitler, and have history change so Hitler never turned evil.