None of the movie Avengers actually fight crime, at least street-level crime that doesn't involve Hydra or terrorists.
You don't see Iron Man, Cap, or Thor going out on patrol for crimes to stop.
The Netflix heroes do but they're persona non grata as far as the movies are concerned (and vice-versa for Spider-Man in their world).
Spider-Man is effectively the only guy who'll swing by and stop a purse snatcher or help the police foil a bank robbery.