I follow what you're saying, but many folks on this planet have far less opportunities than such a trip might provide. Guaranteed food, housing, access to cutting edge healthcare, a likely united community. I'm assuming these ships would be fairly big. It would definitely be different but-- would it be as bad as we think?

Unfortunately, I suspect that any starship that could bring with it all of those services would also bring with it the economic and political strife of Earth. The are lots of examples of democratic states turning into oligarchies or worse in recent history so that can't work in it's current form at least.

The closest analogue in the real world to the ideal that you describe is, I think, Cuba. It does guarantee food and housing, and it does have a remarkably advanced healthcare system plus what is reportedly a united community. Perhaps most interesting of all, it's politically isolated like a starship would have to be by its nature. Even then, one would have to be either pretty brave or desperate to go along on the journey, as modern Cuba has only been around for half a century and that's at the absolute minimum of an intergalactic starship's practical mission duration.

It would be better than living your entire life in a literal cage on earth. But I think it would be worse than even being a slave on earth. A slave can touch grass and hope to run away. A person born on a generational ship would be effectively enslaved (to perform necessary ship duties). You mention 'cutting edge healthcare', but on earth that requires the substantial and diverse resources of an industrial civilization. The research of millions of people and the infrastructure to breed nuclides and manufacture precise machinery. Does this generational ship have a modern chip fab on it!?