Which isn’t a problem in HPMOR, because we’ve been given a number of persuasive reasons why Quirrell wanted Harry alive—he didn’t change his mind about this until he heard the prophecy about Harry destroying the world, at which point it seems he decided to kill Harry as soon as he’d used him to obtain the Philosopher’s Stone.
...or character growth in the protagonist, theoretically.
Perhaps, but you have to get around why the villain doesn’t destroy the growing threat while it’s still weak.
Which isn’t a problem in HPMOR, because we’ve been given a number of persuasive reasons why Quirrell wanted Harry alive—he didn’t change his mind about this until he heard the prophecy about Harry destroying the world, at which point it seems he decided to kill Harry as soon as he’d used him to obtain the Philosopher’s Stone.