I don't have any statistics ready to hand, but my recollection is that most households are not in an HOA, but that most newly–built houses are. It is my understanding that cities have started to rely on HOAs to own and maintain infrastructure that would once have been the domain of the city, and that cities are doing this to avoid raising taxes.
On the one hand that makes a lot of sense. If you want your neighborhood to have a park, but you also want the streets built so that they lengthen all trips in and out of the neighborhood, then the park is really only going to be usable by people who live there. It is therefore unfair for people on the other side of the city to pay for maintenance of that park.
On the other hand, HOAs can turn into drama factories. Too many people vehemently hate their HOA for being petty tyrants.
On the gripping hand, city governments can be pretty annoying too. San Francisco apparently takes an average of three years to approve building permits. A few years back my favorite restaurant (not located in SF) was being remodeled, and the owner took the opportunity to replace the front door. The original was 40 years old and wearing out, so she replaced it with a virtually identical steel and glass door, the kind you can find on commercial buildings from here to Vladivostok. The city spent an extra month hassling her about it, worried that she was destroying the historical character of the town. Madness.