Do we? Some people live in HOAs, and those can even be abusive. Even that little power draws the corrupt. Whether in an HOA or not, we probably actually know our neighbors, and there is actual discussion and mutual consent. Do these actual agreement between people somehow translate to legitimizing government?
There is a massive missing link in your chain of reasoning, particularly when it does not matter if my neighbors disagree with something like whether I drink beer, smoke a joint, or even shoot up heroin if I do not violate their lives, liberty, or property.
Believe me, I know the high school civics arguments about government. I'm questioning the validity of those arguments and the reasoning behind them. How do we get from "I need to coexist peacefully with my neighbors" to "government gets to extort, kidnap, or murder them if they fail to abide by arbitrary laws against non-crimes none of us agreed to in the first place"?
It does not have those rights, because we do not have those rights.
We agree that government is corrupt. Do not think I claim any of those things are lawful government.
However, we both have the right to agree with our neighbors to create an HOA, and decide that only plastic palm trees can stand in our yards. It's stupid, ugly, and would lower our property values, but within our rights to govern ourselves by that rule.
That is what government has rights to do, not rape, rob, and murder people that shoot crack into their eyeballs. Other than such lawful and just agreements we might undertake with our neighbors, there is no just government.
Do we have the authority to impose arbitrary rules on our neighbors, or is this also usurpation? You simply assert we can. Why? Why can no one opt out of even an HOA if it becomes tyrannical?
If all of my neighbors decide they want an HOA, but I dissent, do they have the right to impose it upon my property?
In an HOA, what makes the majority opinion in how to administer it correct, and why is the minority compelled to obey?
I have very clearly said we have authority over ourselves, and in agreement. I have never intimated any other thing. I have instead pointed out that governments claim authority they do not have. HOA's included.
I also vehemently disagree that democracy isn't tyranny of the majority of voters - which is never a majority of the population, in living memory. Just because three of my neighbors tell me to cut my grass doesn't mean I have to - unless I have contractually agreed to abide by majority decisions regarding the length of my grass - which a lot of people do when they buy property in HOA's, to their regret.