Some places are “unincorporated” and don’t even have a municipal government at all.

The way you phrased that sort of implies municipal-government things just don't get done in unincorporated places, but that's not the case. Instead, it's just that the county government handles everything directly. And of course, everywhere in the US is part of a county. (Except Louisiana, I guess, where they're called "parishes" instead. And maybe Native American reservations too, IDK?)

HOAs exist to serve a specific subset of the population who want to own a single family home but lack the ability or willingness to do major maintenance.

There are two major purposes of HOAs:

1. To handle maintenance of shared or collectively-owned property, such as exteriors and common areas of condominium buildings, neighborhood swimming pools, private streets, etc.

2. As the last tactic of segregation: once de-jure segregation was abolished (1917), property owners switched to using racist CC&Rs (deed restrictions) to keep out minorities. The first HOAs (at least for single-family house neighborhoods with little or no shared property) were created to enforce those restrictions. Even after those were ruled unenforceable (1948), HOAs remained popular as a means of creating ostensibly non-racist rules and then selectively enforcing them to harass non-white residents.

And I hate to break it to some of the folks in this thread who think their HOA is innocuous and is just there to make sure everybody's single-family house is presentable: if it isn't reason #1, then it is reason #2. You were just too innocent to realize it.