Superpowers end up in the hands of kids who cause some tragedy through irresponsible use of their powers. Now traumatized, they learn that with great power comes great responsibility. Is that realistic?
Superpowers are given to maladjusted assholes who lash out, killing billions and destroying civilization as we know it.
Some loser gets superpowers and uses them to impress his stoner friends, neither harming nor helping anyone.
You get super-mercenaries running around toppling super-dictators and non-super non-dictators to install friendly puppet governments for whatever new world order lizard person is paying them this week.
Rampant anarchy, chaos. People with superpowers would use it to get revenge on those that have wronged them. The law is no longer able to hold them to any sort of standard. Because you have God-like powers, humans begin to become toys to you. The only difference between good and evil becomes if you treat your 'toys' nicely.
Supergroups don't form. Instead, Superhero warlords form, allying and carving out territory, ruling as a despotic monarchy or oligarchy. Nuclear weapons are attempted to be used, but the supes basically intercept them. Since most foolishly launch them at cities. You get some nuke damage, but not enough. This doesn't work for China, because Global cooling ensues as China effectively falls on its sword massively nuking itself, rather than let the supes rule. Russia launches strategic strikes, but fail. Since supes intercept all the missles and are claiming Moscow, the KGB smuggles and ICBM into Moscow and detonates it. Facing slavery, the US scientists encounter a stunning fact: Supes require massive caloric intake to fuel their abilities. They make a surprise play that the supes didn't expect: The US nukes the mid-west, effectively destroying the food supply of the world. Some nukes are detonated in silos to distract them, while the restis used to destroy all viable farmland. They can't use nukes to kill all the supes, but they can poison the land.
With the bread-basket of the world annihilated, super heroes begin to weaken. Their super powers rely on high caloric intake. Their power slowly begins to diminish as they demand more and more food to keep their powers. Internal power struggles occur between superheroes. The remaining humans band together, and wait for the super heroes to become weak enough. They over power the supes and rape and murder them.
Effectively, the rule of Supes comes to an end through the strategic application of nuclear weapons. Supes become just extra strong humans, nowhere near as powerful as before. Eventually, supe genes mitigate and spread throughout all of humanity. All of humanity has super-powers. This lets humanity go back on a course of law and order, since the playing field slowly becomes equal. Eventually enclaves turn into isolated city-states and food is regulated based on your abilities and loyalty to the state.
This would all depend on just how powerful the superheroes can get and how creative they are. DC and Marvel heroes (A-listers anyway) could basically take over the world and there would have to be a massive governmental response to just have a chance at survival.
BNHA heroes on the other hand are largely dangerous on maybe a street level but couldn't really go much further than maybe third world warlord in terms of sheer damage. Any of them could fuck you up but they're not an existential danger as individuals except if you really piss them off as an individual.
Another level that would be intriguing is if you had Old World of Darkness tiers of superhero to deal with or maybe something on the level of a high end Dnd character. You'd have people who are essentially superhuman and impossible to stand toe to toe with but just vulnerable enough to need to placate the crowd. It would be interesting to write that series and see how the characters change.
It depends on... a lot of things...
How common are powers? 1 in 10? 1 in 1,000? 1 in a million?
Is violation of conservation of energy allowed or do these powers take significant effort/require a source?
Tbh, I wouldn't be all doom-and-gloom about this in any case. If the distribution is truly random, it would mostly be nobody's getting these powers anyway and most people are pretty unambitious. most of the bad ones would just rob banks and shit, most of the good ones would apply their powers for competitive employment. Coalitions would probably form: some good, some bad. But overall I think shit would be fine. Not a lot of people out there desire world domination.