My guess is that Spider-man's a weird mix of street-level and chaotic good/neutral good or something. He doesn't always turn in the 'bad guys' to the police if he thinks they're just having a rough day, but he rarely does more than rough them up enough to tie them. >Punisher, Thor, Ghost Rider, Wolverine, etc.
Spider-man doesn't kill, and I have to imagine one of these guys would want to do in the villains>Capt. America, Iron Man, Thor, X-men
And these guys are usually handing larger conflicts, not street level stuff.
Maybe he could get DD to come around more often, but I feel DD likes to target corruption to fit in with his lawyer schtick. Peter's just a guy who tries to be good all around.