Most companies YC funds do not have the potential to be on a stock market index, because they are features as much as products at that stage and often addressing smaller markets. They are still startups.
YC and VC are very particular avenues for startups, but they are not what DEFINES a startup. YC and VC are the sillicon valley model and that is really actually a small part of the total startup ecosystem, though it is the one that makes the most noise.