Why do people buy shares, other on the fact they are betting on price fluctuation or holding for dividends? People buy oil to run their cars, people buy corn to feed cattle/human consumption etc. But if you weren't able to cash in your shares, why would they be valuable? Looking at Investopedia, as a shareholder you can (1) vote, you have (2) ownership and can (3) transfer ownership, you are entitled to (4) dividends, you can (5) inspect the coorporate book and records and (6) sue for wrongful acts. So dividends are clearly valuable, and apart from ownership the rest of the privileges dont look too valuable. And investopedia says ownership means you have a claim on the assets. What does that mean? What does that actually entitle you to? Holding shares seem to have little intrinsic value apart from price speculation/dividends. For the company that goes public it makes sense because they get a whole ton of cash in exchange for ownership.
Similarly you could ask why people work for money. The intrinsic value of an item is not always how useful it is. In the case of paper, it is valuable because many people believe it to be. Shares are a derivative of paper money. It's the same idea, but with added selection of consumption. Employees are often given stock options as a bonus, this ties them to their position.
Originally paper money was valuable because it could be exchanged for gold. Fiat currencies have always become worthless in every case of history. So if thats true shares are only worth money because people think they are, they don't really serve a function other than speculation. It's then acting as a "money sink" because dollars go in and don't really do anything. Although I suppose a rising share market has the pyschological effect of making people spend more because they are wealthier on paper.
It all depends on the % of ownership that your holding represents. Check the effects of a Carl Icahn on companies ( more often than not he creates fear and uncertainty, if not terror in some CEOs).
Things like dividends, buybacks, mergers/buyouts tend to make the price of shares stay in line with how much they are worth. If they get too out of line those things tend to kick in and bounce them back. That's what shareholders are counting on