People seem to invoke the word capitalism whenever things aren't a utopia for everyone involved. Still, even without capitalism, you'll have to contend with the issue of how to cover operational expenses. Say some, more centralized, agent decides YouTube is worthwhile - how would it get paid for? A state sponsorship made possible by a tax of some sort? Perhaps it would transition to be completely pay-to-play?

The employees and servers are expending real energy keeping YouTube operational. Meaning, whether it's through ads, a more centralized body stepping in, or some other less pervasive, opt-in business model - the thing needs to cover its own costs. I don't think a lack of private property would solve much there.