I was just starting a campaign that was kind of dealing with this. Most large cities have a taskforce dedicated to supervillains, whether at the street level or more. This specialized unit often employ a few superhumans to help offset the their odds a bit. In the campaign I've been working on, the city has been a bit overpowered by villains and gangs. So they sponsor a hero team that works exclusively with the police to help protect the city. Local police powers, access to the police database, and a crash course on law enforcement are the basics that everyone gets, and they answer to a special liaison officer that answers to the police commissioner. What kind of threats do they handle? Pretty much anything the city may throw at them. From villains akin to Spider-Man's rogues, to juiced up gangs, to Kingpins and gang wars, to the occasional Magneto attack.
I agree that, in most cases, setting a street level tone would be my normal go-to for such a game. But I'm trying something different to see how it evolves.