I think that's OK. Another thing we need to do is bring criminal liability for the board and the CEO for corporations. Probably not civil but definitely criminal.

The idea is that antitrust regulation would kick in, but that's unfortunately not a priority of our government in the past few decades.

Presuming the company fully owned (or with some sort of pro-rata split) you could tax the parent company for the total of their holdings. If they truly were separate companies, well, that satisfies the OP's objective too, no?

(Note I'm not a big fan of corporate taxes in general, I'd rather we not tax corporations and tax individuals more aggressively. Get rid of special rates for capital gains and have a much more progressive individual tax system.)

That sounds good. Then, as long as control becomes more diffuse through the public markets, the incentives are in place for them to start working with everyone else in the market, not just their corporate parent.

Not trivial in practice, but sounds like it would be much better if we could figure out a way to make it happen. The first step towards more federated standards and interoperability is to have a larger number of players in the market.