There are a few insuperable problems with society vs real superheros as I see it.
For the sake of argument, let’s assume a valid superhero with real superpowers (unlike some people who want to live the life so badly that they go around dressing up as superheros:
Real-life superhero, but who don’t actually
have any superpowers).
The first problem is one of targeting. Assume there is a crime occurring somewhere in town. Superman doesn’t have a problem finding such an occurance, he has super-hearing. All he has to do is listen. The police don’t have a problem finding crimes either, because people call them in. If the superhero doesn’t have super-hearing, and nobody is calling in crimes or disasters to him, how will he know something is going down until long after the fact? Does he wait to read about it in the paper, see it on TV, or hear about it on the radio?
The second problem is the negative reaction of the police. The superhero has not been trained in arrest procedures, nor does he have any place to put his villain after he stops him. Leaving the villain tied up for the police would probably accrue a charge of kidnapping or false imprisonment for the would-be superhero. The police will probably not take kindly to interference in police business, and any slip-up, like pepper-spraying the wrong person, will result in a lawsuit. This isn’t a problem for Spiderman or Superman because they typically take off after either leaving the villain enmeshed in webbing or knocked out cold. Nobody can catch them or do anything about it either. Most other comic-book superheros are the same way, but any diminution of one’s powers of escape would leave one vulnerable to police anger and irritation, to say nothing of litigious victims of any mistakes. Also, comic-book cops simply take Superman’s word for it that so-and-so is a crook. In real life, it wouldn’t work that way. Superman would have to fill out a complaint or other paperwork.
Police too have problems with litigation against them, but the city goes to bat for them. That’s a pretty big deal, to have a city, county or federal government behind you.
A third problem is the mismatch between the superhero and the villain. If there was actually a superhero with real honest-to-goodness superpowers, who would he fight? The local crackhead? A shoplifter? A crooked politician? A spray-paint vandal? Most villains would be very much outgunned by a real superhero, so much so that such a mismatch would be laughable rather than a source of drama. Lex Luthors are rather scarce in the real world, to say nothing of characters like Doctor Octopus, the Green Goblin, or the Parasite (able to steal Superman’s powers with a touch). Real police work is more like being an orderly for a psychiatric hospital, or a social worker, than it is like being in one gunfight after another. Lots of cops never have to draw their guns in anger for their entire careers.
The takeaway from this is that society won’t have to respond to comic-book-like scenarios because they will never arise, or at least not in the foreseeable future.
In the more distant future, in 10,000, 100,000, or 1,000,000 years from now, perhaps there will be some issue like this that really could arise, but it’s also likely that everything else will be so different by then that we wouldn’t even be capable of grasping most of the ancillary issues, thus we cannot say how a society in the far future would respond.