It’s not a Constitutional issue either way. Your right is your choice of neighborhood, NOT to force on the neighborhood what YOU want - be it an HOA or nothing.
And HOA has nothing to do government - it’s a mechanism of self government of a very narrow swath of life. I can understand not wanting to live under an HOA, and I can understand wanting to also. It’s called liberty, but there’s zip zero nada analogy that you are trying to make.
Good job contradicting yourself within a single sentence.
By the way, wasn't the United States Constitution intended as a mechanism for self-government?