I have spent a lot of time recently trying to nail down the MHA timeline as it relates to reality. Present Mic quotes Napoleon, which means that until that point at least, history is as ours.
However, it cannot be that the present is as it is now, as assuming that each generation of One for All used it for at least ten years (and about 25 for All Might) one can put the Quirk Age as lasting at least 100 years. That would likely have eclipsed the invention of nuclear weapons, which are there as a trope within the combat trial.
Therefore, I put MHA in the somewhat distant future. Somewhat supported by Mario references that mention it as a really old thing, but I digress.
However, that presents an interesting question: How would that have affected entertainment? Would superhero comics and movies have survived that much time with their subjects being reality? Could they even?
Consider another thing: if DC and Superman survived, and then there was a timeline of any sort where Superman went evil again, then how does that reflect on the hero industry as a whole, or even All Might specifically? What was a somewhat political commentary veiled by the ridiculously impossible becomes a very real warning on what could happen should those hailed as heroes turn evil.
That doesn't sound like it would be allowed for long. And the more heroes and Quirks show up, the more classic comic heroes might start looking like parodies of reality.
While that doesn't necessarily mean that Marvel and DC wouldn't survive, 100 years is a long time to survive without major changes. Anime would also be majorly affected.
Partly in order to just say that classics would stay classics, I will say that they just died out, and are referred to as the "old stories." After all, even if the sources all survive, the stories that would come out in the Quirk Age would undoubtedly be different. Exactly what would be different is hard to say, but stories cannot be unaffected by the cultures and political/social/scientific climates in which they are developed.
For that last one, think about the original comic origin of Spiderman vs. more recent stuff. They originally said radioactive spider because it was known as a mutation cause, but now say genetically modified because it makes more sense with general scientific knowledge.
Anyways, that is what I mean by the "old stories." Bygone relics of a dead era.
As an addendum, I think that people like Batman, Iron Man, and Captain America, as "Quirkless," definitely wouldn't survive in their current forms. This world has shown its hostility to the Quirkless, and those that straight up destroy powerful beings with nothing but experience and intelligence wouldn't fit the general narrative the world is trying to sell. Cap would become more like All Might, Iron Man a technomancer, and maybe Batman too.
Why do I keep making these essays? Well, in part because I keep thinking about it, and it isn't always important information that fits into the flow of the story. I'll include the same information as it comes up, but I need to get this out.