The following is my briefing on how it would be bad:
- Peter is no longer an orphan and has little to no reason to feel like outcast. Therefore if A. he continues being an outcast, he's a dumbass and an unlikable character or B. if he isn't an outcast then becoming Spider-Man doesn't change his character in any significant way.
- Uncle Ben and Aunt May did not choose the responsibility of adopting Peter. It was thrust upon them. Therefore their love and compassion is a feat of their own goodness which they, in turn, pass onto Peter. If they are his parents, Peter was likely an accident (statistically) and they are almost required to love him.
- Uncle Ben's death wasn't the only loss that Peter has grown from. While we all know what Ben's death taught him (with great power comes great responsibility) Captain Stacy's death taught him the risk that comes with being a hero, and Gwen's death taught him that sometimes things go wrong and we can't do anything about it. But his parents death taught him life was precious long before he ever became a superhero.
That's all I got right now. I'll try to think of some more.
- EDIT - More specifically and more relevant recently (with the new ASM movie) without the death of Peter's parents we lose an entire potential story arc and element of mystery to Peter's life.