> I wonder if there's a cultural element to it: do people support democratic processes in their families, neighborhoods, companies, etc?
I don’t think that’s right - although some on the left have advocated “industrial democracy” or “workplace democracy”, it has by and large failed to take off - many democratic countries it doesn’t really exist (beyond rare exceptions), and even those which have some semblance of it (e.g. works councils in the EU) it is in practice rather toothless, comparable to the powerless “advisory” legislatures established by some Middle Eastern monarchies
Families don’t function democratically-the parents negotiate things between themselves and the children don’t really have a choice in it until they get old enough to leave the family home and fend for themselves.
My neighbourhood isn’t a democracy - yes we have an elected local government but it covers a much larger population and territory than just our neighbourhood. Even if one’s neighbourhood has something like a “homeowners association”, that’s usually timocratic (government by property owners) not democratic (government by the people) since renters don’t get to vote, adult dependents of homeowners don’t get to vote, a couple may jointly own a home but they get only one vote not two, some wealthy person owns five homes so they get five votes, etc (and sometimes even weighted voting, so rather than one property one vote, more expensive properties may give you more votes than cheaper ones)