Unfortunately in my experience it's the exact opposite. Here they're used and abused by exclusively rich, mostly-white neighborhoods to keep them that way.
I've lived in both HOA and non-HOA neighborhoods. If there's a barrier to entry such as price, then generally a more successful (and hopefully more refined) type of person will move in, and generally the homes will stay nice-looking without rules. Without that, then an HOA to try to maintain an aesthetic baseline can be very helpful. All the homeowners benefit from maintaining an attractive neighborhood, in that their home values will be higher.