You missed one final point. You don't need a new government seizure for the starting premises to result in a state AI run capitalist economy instead of capitalist AI run capitalist economy. The existence of pre-existing taxes is enough. If AI was better at capital allocation decisions (investing) than "investors", and a 30% top income tax rate (or even 10%), it would have a long the long run advantage over all private investors.

In this world, a government running a sovereign wealth fund that doesn't pay taxes would inexorably grow it's share of the economy. Now massive "seizure" needed, just plain old taxes.