Demand doesnt allocate resources... price and expected economic profit does.

Thats literally how the whole economic system functions.

Yes its decentralised still. And the idea is that competition is the force that keep things in check - with shareholders interests taken care of with the focus of manager's being to optimise for whatever makes the owners better off.

At the extreme with 'AI' - there's no need for firms to exist.

'Power to the people' was always transitory - do you think the govt is dumb? Lets take a simple form of capital: cameras. Would cheap cameras exist without the private sector competing for shareholders interests? Probably not.

They aid and abet it. It benefits their own interests. This game goes on until the govt no longer see's the need for a private sector anymore.

"Then Lenin concluded that if you will always have concentration of power and some folks doing centralized planning, it might well be the state."

This is exactly where things are heading.

Theres no need for firms anymore at the extreme - the govt can own all.

Dude we aren't performing some nonsensical calculation in our brains.

Mathematics is an invention of humans.

Not sure about "nonsensical calculation", but our brains perform computation (read: they transform information). In fact, that is what the brains are for (see: biology 101). As for mathematics, I am with Galileo: it is the language of the universe. Of course, we "invented" its silly glyphs and the like, but those are secondary. My 2 cents.