Capitalism is defined by having the capitalist, who provides capital, and without the ability to sell their share of stock it's difficult to see what the value would be. So you kind of require stock markets.
Edit: which is why it's odd to call China communist. They have 3 stock exchanges. They're really a capitalist single-party state.
In the U.S. we have mistaken Capitalism for a religion, and so it wags the dog, so to speak. Since our founding we have made some attempts at finding a balance between our use of the tools of Capitalism and socialism (in more the Democratic Socialism style, rather than the Communism style), and we had a good run in the decades after WWII. But starting with McCarthyism, and really picking up under Regan we have prided ourselves on adopting Capitalism as a religion, and it really shows up in both the income inequality as well as the increasing role of (and corrupting influence of) money in our politics/government.