... it's almost as if Mohammed was an economist who foresaw all the economic problems of the 21st century, and built protections around them.
Peace be upon him. It's simply more evidence of his prophethood :)
(1) Right now, virtually everyone agrees that individual choice is important and all humans are born with equal rights
(2) If they don't, it's often possible to come up with solutions which work for everyone. The problem is when people jump to solutions ("democracy") rather than problem-statements and first principles.
The early US is a good examples of -- actually quite exactly -- your contrived example. The South had slavery. The North didn't. There was an overarching federal government which dealt with military and foreign diplomacy. It worked for a bit over a half-century until it didn't, mostly for reasons unrelated to why it worked as long as it did (the expansion of northern culture west upset the design, as it had an upper hand in congress).
My claim is that there are systems of government which do a better job of protecting individual choice and equal rights than capitalist democracy. My claim is that if you articulated your value system completely (probably not on a web forum but over an hour-long coffee), we could probably design a better one around your values, which also did better for most people's values. My claim is also that if you've signed an NDA, you probably don't have all that much individual liberty.
That's a contrived example, but this kind of disagreement is very common in discussions about government and society. If you believe that individual choice is important and all humans are born with equal rights, and I believe that individual choice is unimportant and some humans are born superior to others, we are never going to agree on an ideal form of government. We can have full agreement on the facts and full disagreement on what we consider to be a "good" outcome.
You mentioned game theory, but you can't design one model that will satisfy one person who wants to maximize outputs for all players, one person who wants to weight players in different castes differently, and one person who wants to set a hard cap on all players because too much material comfort leads us away from God.