Well, companies do sometimes make further public offerings.
Stock trading also provides a somewhat objective measure of the value of the company. For instance, if MS wants to buy Yahoo, how much should they offer? Without the stock market, it's tough to tell if they are lowballing or paying a premium.
You're spot on that the market is a means of both creating information and disseminating information. Information is key to game theory. That's where sigma algebras and filtrations start to creep into theory.
Stock trading also provides a somewhat objective measure of the value of the company. For instance, if MS wants to buy Yahoo, how much should they offer? Without the stock market, it's tough to tell if they are lowballing or paying a premium.