I think your mistake is reading Bridgerton as utopian political fiction and not a romance film with a fantasy drawn around combining exaggeration of a few specific facts of Regency England with a couple things drawn from modern Western race and gender politics is the context and engine of conflict.
> There's no classism or anything structural in that show
There is fairly intense classism in the show.
> In that sense it's no different than Hamilton, where you had, ironically enough, an almost all POC cast represent not a single POC character.
Minor nitpick: Hamilton, in fact, has a single explicitly-named on-stage POC character, though the part has no lines.
Major nitpick: you...did not understand a few layers of metaphor in Hamilton.
> superficial diversity in place of actually talking about race, class, and so on.
Hamilton rather directly talks about race, class, “and so on”.
I mean how do you say any of this is American politics and not British/Western European politics? Racial inequality, women's rights, and class structures are not just American things.