I’m dubious about what a stock market can do for a company once it’s had its initial public offering. It’s like betting on horses. Betting up a horse does not make the horse go faster. More topical, the horse’s owners don’t benefit from the bets.
Buying control of a company does allow one to make changes with the expectation that the "horse will go faster". There are certainly some practical aspects of a person with one thousand dollars trying to control a company worth a billion dollars. They must share control with a very large group. But very expensive companies get bought in their entirety all the time.
As for the horse's owners not benefitting from the "bets", that is simply not so. If the market place is willing to "bet" more for your stock, you may either sell what you own at a huge profit or issue new stock to undertake expansion of the business. Almost every large company and many smaller ones provide "stock incentives" to their professional staff. The staff benefit directly and sometimes very greatly by increases in the "bets".
Many progressives lament the large payouts that some CEOs and other officers make when their incentives are tied to rapidly rising stock prices, as if talented people would be willing to work for a fixed salary when they are responsible for the fate of a large corporation.