David, it’s a tough nut you attempt to crack here and it’s a good effort. Congratulations.
In my opinion the argument you are making fails because in your premises you can, in my opinion, easily substitute the word ‘socialism’ with ‘capitalism’ (and vice versa) and the claims would still appear to remain true.
I believe that free markets and fair societies are locked in a competive symbiosis: individuals struggle to get an advantage in the market and societies attempt to prosper as a whole which requires market-rules and regulations.
Both, markets and societies, are prone to be corrupted by those in power.
Whether that power is derived from financial- or societal status is in my view a moot point as one begets the other.
Anyway that’s just my 1 cent’s contribution (head and tail) and an oversimplification 🤗.