to compare with europe: as far as i know germany or austria don't have the equivalent of a HOA, but what is allowed and what isn't is defined by local law. the closest example i could find are rules a landlord is allowed to impose on their tenants. for example, if i rent a house with garden, then the landlord can demand that i take care of the garden, but they can not specify how often i am supposed to mow the lawn or how high i let it grow.
if not even a landlord can make such rules for their own property, then a HOA would have even less chance to make such rules for homeowners.
that said, local laws can be quite far reaching, especially when it comes to aspects that affect the character of a neighborhood which includes rules on the outside design of the house and the front yard. not something i am happy about myself. beyond that these rules are mostly about things directly affect and cause problems for the neighbors. otherwise a homeowner has the right to do whatever they want on their property.
as for the freedom to choose an HOA. no such freedom exists. because my choice of where i live is not defined by the HOA but by other considerations like location and cost and most importantly, availability. the argument that i could have moved somewhere else if i didn't like this HOA is not really reasonable given the housing shortage in most places.
the right to live somewhere trumps the freedom of association