Because the Avengers typically have Iron Man as a permanent member and other geniuses like Hank Pym, Beast, T'Challa and others rotating in and out of the roster. Peter's role as a "smart guy" would be fairly redundant.
Also, people who read the Avengers aren't reading for civilian interaction; they're reading for superheroes. If Spider-Man isn't going to be a part of the team, no one's going to care if Peter Parker is. They want Spider-Man to be a front line role.