Everything you say here could be said of $100 bills. It is a social convention because trading things that have real "intrinsic" value, like goats or cars or houses, is too difficult. The fact that the system is vastly superior to barter is what keeps the whole thing going and keeps people from losing interest.

Why you want something with no intrinsic value is because others do, yes. Because we've all agreed to trade those things for other things that do have intrinsic value. You want the stock, not for itself, but for what it represents should you choose to exchange it for something you want.