You have to always remember that stock shares represent not only profits but control. Small-time investors don't have very much power, but big-time institutional investors get seats on the board of directors. Likewise, when one company acquires another, stock may be acquired or swapped or whatever else.
Further, you have to look at the long-term value of a share of a company versus other sorts of long-term investments. You can keep your assets directly as dollars or euros, but then inflation will reduce the value of your holdings over time. You can keep your assets in a money market account, which means you really own treasury bills (i.e., government-issued bonds). You can keep your assets in real estate, which may or may not appreciate over time, and which can have ongoing maintenance costs. You can keep your assets in precious metals or oil or whatnot, but those have volatility that may not be appropriate for most investors. Stocks, by and large, have no maintenance costs, can be selected for desirable volatility, and tend to outperform inflation over the long term.
Given that you need to park your assets somewhere, and pretty much any asset you might own is going to be abstract, why not have a big chunk of your assets in stock?