There are plenty of companies that are private that have large ownership shares. The point of going public is to raise capital buy relinquishing some ownership. Owners don't want to give their shares unless they have to. If there were mandates to sell out of a company that you started and at a stage before you realized the gains on the capital you raised, it would incentivize companies to stay private and find their funding through private channels.
I agree with what you are saying. But by relinquishing ownership they are gaining the ability to receive far more capital than they would without the public market from what I understand. If this is reinvested in the business it allows said company to grow to levels that would not be possible as a privately owned company. Even the largest privately owned company, Cargill, is making interesting restructuring moves that point to it possibly going public.
I'm actually fine with companies staying private because I fundamentally believe this seriously restricts their growth. I do not think a company like Amazon, Facebook, Microsoft, or Google (20% of the S&P 500) would be able to reach the size they did without access to going public.
Of course I fully admit I could be wrong and would love to hear interesting arguments why.
I think the growth part can be the case in some instances, but not all. I don't think it's a fundamental restriction, but maybe more common in the private world.
The voting rights don't necessarily come with every share, nor are they evenly distributed. So you could raise capital through non-voting shares and retain the ownership.
Another thing to point out is that the size of the company based on the market cap and share of S&P500 doesn't really have an influence on the capital they raised by issuing shares. You have companies that have 100s of billion in market cap that only raised one or two billion through stock offerings. Private companies are also able to raise that sort of money too, like SpaceX recently did. With this in mind, how does staying private restrict growth?
Even if you required a buyout of the majority or minority (10%+) owners, you still wouldn't solve the problem. In fact, you could create a bigger funding issue because you aren't using the capital raised for expanding the business but for paying out. For example, you might want to raise $100M, but if the buyout requires the owners to sell a substantial postion, then you might need to raise $400M.