There's no private property without "central planning" (as you characterize it) of some form.
Please don't combine further arguments (which suggest you want to continue the dialogue) with a poisoning of the well. I've enjoyed our mini-conversation so far; if you don't, that's fine, but there's no added value in this part of your sentence.
> Your characterization of the US as "centrally planned"
In my opinion, the key metrics of central planning are the size of government (e.g. % GDP) and volume of its regulation. The point at which these become excessively centrally planned is hard to define. In my opinion, they have been consistently growing over the past few hundred years in the U.S. and are about 50% and excessive, respectively. I doubt they will cease to stop growing until collapse or malaise.
> There's no private property without "central planning" (as you characterize it) of some form.
I did mention "minimal" central planning; however, again, you're making an assertion of political philosophy. I do not believe private property requires central planning. See: The Problem of Political Authority by Michael Huemer for example.
This is why political philosophy is important. The United States was largely an experiment in political philosophy and it succeeded... temporarily.
Unfortunately, given that the modern world is largely run by either state-managed socialism or state-managed capitalism (neo-mercantilism), there will be no evidence to evaluate your hypothesis on Earth unless there is a mass depopulation (let's hope not).
In my opinion, we will only have new political experimentation and innovation after we become a multi-planetary species. Political experimentation on Earth is too risky.
Until then, pay your taxes to appease the increasingly dystopian and insatiable "leaders".