The stock market's output is difficult to see, but it is there: they compute the value of stock. Why we need to know the value of stock to such fine resolution in time, I do not know.

The bigger benefit of the stock market is that it provides liquidity, which is one of the major appeals of owning listed stock - that you can liquidate it quickly/easily/cheaply.

The benefit you mentioned - pricing stock - enables companies to issue new stock at a fair market valuation. But that's secondary to letting people buy/sell stock easily.