Don’t confuse yourself. HOAs are in addition to state/county/city regulations. A lot of local governments allow HOAs to enforce additional quiet hours or other things.
I’ve never lived in a HOA that had to maintain roads, sewers, or street lights. All the infrastructure is covered by the county or city. Neighborhood pools, playgrounds, and common areas are HOA. That’s in addition to local parks, aquatic centers, and all the other local public service stuff the county and cities provide.
Our lots are 2,000-4,000 square meters or more.