It's certainly overly broad in many circumstances. I've lived in a townhome community with overly aggressive management.

However, "There is absolutely no reason why a single family house needs to be in a mandatory HOA" is easy to refute.

HOA's provide a way for managing shared infrastructure that would not be feasible for a single home owner. Common examples of basic infrastructure include roads, storm water management, lighting, and even community wells. I would argue that is the primary purpose. Not all neighborhoods are in a municipality either.

Not all neighborhoods are in a municipality either.

why is that? and why is the county or state government not taking over the responsibility then? for example in germany a democratic local government is guaranteed by basic law, so a neighborhood outside of a municipality is practically not possible and considered a violation of basic law.