> 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?

Yes, that is explicitly and exactly the reason municipalities exist. In the U.S. they are typically made up of elected and appointed representatives and they manage public space and services in their boundaries.

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.