Every company doesn't have to be public. The US taxpayer underwrites US securities markets, and companies that trade on our public markets have access to some of the deepest pools of low-cost liquidity in the world. But companies are obviously free to list elsewhere.

> the number of public corporations is already in decline.

Separate problem. IIRC HBS studied this and basically the issue is we stopped enforcing our anti-competition laws a while back[1]. So we end up with a fraction of firms that each sector would financially support. Both because it creates giants that are much harder to compete against, and because it allows mergers between competing firms that AFAIK could be deemed illegal under existing laws.

1 - See, for example the Robinson-Patman Act, whose dormancy allows big box retailers to exist. This law has never been repealed.