most HOAs manage a tiny amount of communal green space that should have been turned over to become city property, but was held back as HOA property to give the HOA a reason to exist.
You are just making this up at this point. Why do you think the city would accept property that they would have to legally maintain and be responsible for, when it is generally isolated and (largely) accessible to only a specific neighborhood?
Mostly I don't understand why an individual neighborhood would need it's own out of band election process (that typically allows people to gain tremendous power and authority without anyone voting for them), and representatives completely decoupled from the state or government but often times acting in parallel.
Come on, at least try. HOAs (typically, your word) have elections. Someone doesn't just walk in and declare themselves the association president.
I think we have the wrong units of measure for government size. I live in a county where the lines made sense 200 years ago: Everybody in the county can ride their hose to the courthouse, file whatever they need and be home in time for super. These days everyone drives and can be there in half an hour or less. Instead what I care about is the metro area. I want a unit that ensures my transit system is a coherent whole, the water supply is cheaper to consolidate to one large entity vs many small ones.
There is one suburb near me where some people would have to drive 25 minutes to get to the city library - most of that is uncongested highway. I really need a smaller unit to own and run a library so kids are always in bike distance. That city does a good job of scattered small parks but there is one complex with large fields for softball - if you don't live close maybe you shouldn't pay for something you don't use. I want parks owned by a smaller area government that can bring my neighborhood something they don't have. - HOAs often serve that. They just have a poor legal structure.
If you own part of a shared walls building then a corporation is required to manage that. You have to pay your share of the share costs. However the corporation should be limited in what else it can do, but it must exist.
You can put in a special district, that's an HOA under a different name, with even more government powers and bureaucracy costs. For example, you vote on stuff via the general election, they can seize your home for unpaid property taxes, they can impose zoning laws, and in some places they can impose criminal ordinances (dog pooping in the park).