There's the attractive nuisance part. There's collateral damage. There's the point at which you speculate that DC has Coast City, Gotham, Metropolis, Central City, Fawcett City, etc. because the presence of supers has encouraged spreading out over the land. Superfights actually being attracted to the city.
One can see why a super would want a secret identity. At that it would be of some help in that the most the villain would know was that City Hero is associated with the city, not his street address. Though it would create trouble as the villain tried to draw him out. From the law's point of view, however, that would be endangering lives.
Any significant number of supers would probably have them concentrating themselves in a building or compound pretty rapidly, especially if secret identities are impractical for whatever reason. If they don't developed rapid transit, and don't have speed abilities, they would have an interesting time working far away, though, from crime fighting onward.