When Disney purchased Marvel, they looked through the properties acquired to see if anything jumped out as a good subject for a Disney animation feature. I had not heard of the Big Hero 6 comics but I understand it was altered just a little. It takes place far into the future and is a property of Marvel/Disney so it could be the distant utopian future of the MCU+ after the heros of the Avengers, and X-Men, have won but not after there has been substantial damage to the infrustructure of the world and mild stagnation in the advancement of technology.
In the time of Big Hero 6, supervillainy is a thing of fiction where Fred is the character with any knowledge of comic books that he recognizes the villain as a danger beyond law enforcement's abilities. He has a tendency to say very off the wall things that seem crazy like saying he has demanded one of his friends turns him into a monster and it is brushed off has part of his cookiness, however, his strange ideas end up being true. He has a friend that does turn him into a monster and the villain is well beyond the capabilities of law enforcement.
This could be the result of a broken clock being right twice a day, or it could be that he was a history major and his friends are engineers. The engineers are unaware of the paterns in history as they have focused their energy on the sciences and don't know the history of superheros changing into monsters and fighting villains with advanced skills, technology or powers. This knowlege is less common in nonhistorians because it happened so long ago that it has fallen into academia much like fallen empires, natural disasters, or forgotten technologies today.
In the Big Hero 6 time, large cities like Tokyo and San Francisco have gone through so many city destorying events, and possibly even great earthquakes or land changing events (I think the Mole Man in Fantastic Four created earthquakes as an attack) that the two cities have merged or rebuilt together.
Additionally, the technology in this world is reminiscent but not far advanced from what we see now. This could be a result of cultural backlash from the advanced technologies seen in the MCU+ from Tony Stark whose technology has already turned against him in Ultron to the point there may have been a referendum on technology like there was with mutants in X-Men (and possibly heroes in Civil War, at least that's what happens in the comics version) where there is a registration and restraint on people with special powers.
Technology isn't completely quelled because Hiro in this story is able to go into engineering and is able to create very very small robots that fill several garbage cans. He is able to either find or purchase large amounts of raw materials to make his technology in his garage meaning either he has a very substantial inheritence from his absent parents (let's face it, it's Disney, they have been tragically killed) or the materials are readily available in this time. Technology hasn't completely stalled from the time of Tony Stark, but has become more efficient and small to the point where young students have the materials that their inventions are organic like the simultanious invention of cinematic film in France and Germany in the late 1800's and not a miraculous leap in science.
This seems to be a repetition in culture in the MCU+ so I would not be surprised if it leads to a resurgence of super heroes and villains in the time of Big Hero 6 and could even be the kick off of one of my favorite lines of Marvel comics from my youth: 2099, except without the terrible futuristic slang. Oh shock!