I don’t understand why concentration onto a single capitalist or a small group should destabilize the system.

A hunter gatherer tribe can live by itself. The world run by a capitalist could as well.

You're confusing the ability for non-capitalist systems to function without circulation of commodities as their basis with the ability for capitalism to do so. Capitalism functions by this, it's how capital is valorized.

https://en.wikipedia.org/wiki/Capitalism

The single capitalist would still own the means of production.

A "capitalist" system where you have a single person that owns everything is both structurally impossible (similar to anarcho-capitalism) and also not capitalism. You've gone beyond the relations of bourgeois and proletarians into a system owned by a single autocrat, which would immediately cease. Capital isn't circulating, and it isn't being valorized, and this one person could not possibly get everyone to go along with treating them as god-emperor.

These kinds of hypotheticals will never come to pass, and thus it's pointless to discuss beyond entertainment value.

The capitalist could buy everything for a penny. But they don’t have to. They own everything and can pay workers the wages for the workers to survive. But then the capitalist sells the goods for them at the stores at the prices that reflect the effort to produce them if the capitalist wants efficency, or any other price depending on the goals.

Market efficiency doesn't exist here, there isn't a market for labor. It's one capitalist. Prices don't come from thin-air, and the capitalist has no use for money because they own literally everything. Systems of accounting would not work here.

Make it a hundred.

A hundred competing mega-capitalists would still be close to collapse, but could feasibly exist. They would compete and actually be able to valorize their capital, the way capitalists exploit workers today.

In which way? Wiki couldn’t help me.

Simply imagining a society doesn't mean it can actually exist. Anarcho-capitalism can't exist because the state is what legitimizes property relations. Same with your example, both would fall apart into something new.

Decay lets some people suffer. Coupled with wars and fascism the system can still be stable. There must be something in humans that makes them want to cooperate. Organized suffering people alone will disperse when the suffering is over.

Humans naturally do cooperate, and we've seen workers organize to establish socialism. Further, fascism doesn't really stabilize anything, and neither does war, it only temporarily buys time while accelerating revolutionary fervor.