There are certain fiduciary obligations that CEOs hold to shareholders. But on the flip side, if someone opposes the transition of privately-owned companies to being publicly-owned, then their position is that only the wealthy, those who can outright own a company rather than only part of it, via shares, may own companies. That seems quite like a policy exceptionally loaded towards the wealthy. It would make capital much harder to get, so it would be harder for someone who wants to start a company to do so. Only very wealthy entities – stuff like very wealthy families – would be able to own companies of any significant size. They would have little competition for their capital, and would be able to demand extremely favorable terms for it. Less-wealthy people would be intrinsically disadvantaged by their inability to must outright buy companies. Less capital availability would tend to impact wages negatively.
It seems to me stupendously at odds with the sort of thing that I would expect someone on the left end of the spectrum to want.