> That wouldn't make us more free, it would just transfer control out of the neighborhood and up to the City/County/State, where your control over your own neighborhood is transferred to people who don't live in the neighborhood. Does that make us more democratic?

It can and we have decided this many times. As example - nationally it's why a neighborhood can't decide to be "whites only" anymore. "Just convince your neighbors" wasn't working out everywhere so people convinced enough it was better worth deciding once instead of by location.

Of course it leaves more nuance than "all powerful HOA or ban" when it comes to voting on how society should be allowed to work. E.g. people can want building codes to protect general health and safety, especially in context of needing to provide emergency services when things go wrong without wanting to specify how often you need to paint the garage door. An example more relevant to the useful portion of HOAs would be wanting to allow them for community pooling for better street cleaning/clearing or a community bus stop for the kids while not wanting to allow them for what color the fence is (coming back to the GP).