What exactly does the button define as a “problem”? Does it involve reaching into everyone’s heads and rewriting their personalities to make them agreeable? Or maybe it sees something like the Higgs field not being at its ground state a problem, and induces vacuum decay to solve it, destroying the universe as we know it. Even getting that 1% might cause an enormous ethical problem or kill everyone since it’s so vague.
I think the question is pretty clear, it creates such a world where everyone is happy. If the method was unethical, surely someone would be unhappy about it and therefore it's probably ethical. And obviously the universe being destroyed would be a problem for people so that wouldn't happen.
There’s no way to make everyone on Earth happy. There are too many conflicting ideals. How would you make a Neo-Nazi happy on the planet at the same time you make an Antifa member happy? And you can’t say to kill the Neo-Nazi because that’d make someone unhappy. Someone’s always gonna find a problem with something unless the button makes us not care about it at all.
You can say that, but it’s equally likely that a world where nobody has worry or need for worry would be one where those people do not exist at all. Removing the problem is, in essence, solving it. As would be my original worry, being that simply rewriting everyone’s personalities to be more agreeable and not at all care about the change inflicted upon them would accomplish this goal. My point is that without knowing what such a world would look like, it’d be foolish to even consider it.