I don't see why it would have to be though. A bunch of oddballs could certainly get together and create one to protect diversity in their neighborhood from a normie invasion.
For the same reason why very few companies are worker owned co-ops: people suck and capitalism doubly so. That's why we very rarely can have nice things.
In the case of HOAs, the bad ones (which are the vast majority of them) exist to extract profit (in the form of increasing property values, fining anyone who doesn't follow their petty rules, and sometimes even take someone's home for breaking the aforementioned rules) and exert as much control over people as possible.
In the US at least, laws regarding HOAs are a grotesque combination of under-regulation and regulations specifically crafted to FACILITATE abuse rather than discourage it.
Perhaps, but as long as there is no law that says you can't have an HOA that fines you for having a McMansion with a monoculture lawn instead of a natural one, it's at least possible in theory.
I pay an HoA, its like $30 a year. While they dont encourage it, they dont care either. They really dont do anything except twice a year they bring out garbage trucks/dumpsters to the nearby school to dump/recycle things too big for a trash can.
In Germany the city does that at least in smaller cities.
Twice a year you can put all stuff that doesn't go into regular trash out at the street and it gets collected. Think broken furniture, old electronics etc. People empty their garages and basements of all the stuff that accumulated.
It's common to have a walk through the neighborhood on these days to see if there is some cool stuff in there. Got my first skateboard that way as a teenager.