Intrinsic Value of Shares

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.