Free market capitalism and corporatocracy are two opposite things. (Free markets don't exist without strong institutions and regulation)

I don't know how you can say that. What does "free market capitalism" entail according to you? Wikipedia's definition is just a ruse to be able to claim that free market capitalism is sane, but you can't exclude a governing authority and monopolies at the same time, because the latter always arises. So, in reality, you have to choose, and if you choose absence of authority, corporatocracy is an automatic extension of free market capitalism.

Every unmaintained system degrades. That's next to a tautology. In my opinion, the base problem is modern technology itself that creates the capability for widespread wealth inequality and social fragmentation, without needing real labor or social bonds anymore.

I think the latter problem already existed 1000, even 2000 years ago.

But maintenance requires supervision, which seems to contradict "free" in "free market capitalism." Without restrictions, greed makes corporations (or armies, or the maffia) seek influence at the highest levels of governance.

Only in the minds of people who make capitalism a religion. It has always been like this, early capitalism was even worse with dirty money buying every politician they could get their hands on. Just read anything about the US in the end of the 19th century.

They're both capitalism

You are against private property rights? Because abolishing the right to owns things is the only way to prevent any form of capital accumulation.

Of course not, workers' rights to own and democratically control capital is paramount.

Real free market capitalism is a real as working communism and have both the same underlying problem: people.

They lie and cheat to accumulate power