That's a good question, and I don't have a good answer, but I don't believe the answer is advertising. Not because of any anti-capitalist aversion to it on my part, but because the web wasn't designed to allow for it, and I believe the model is doomed to fail in the long run.

Every other media paradigm is centrally controlled and has its equivalent of Arbitron/Nielsen to extrapolate audience size and attention through polling without directly interfering with privacy or taking control away from the viewer or listener. Unless I'm wrong, advertising on the web requires ever increasingly intrusive and fine-grained analytics to accomplish the same thing, in a medium which is designed to give the end user the ability to arbitrarily filter responses.

In my opinion, the only reason advertising ever worked on the web to begin with was that neither browser makers nor the browsing public were savvy enough in the beginning to do much about it, but now ad blocking is becoming more and more common, and the browsing public is less and less willing to tolerate ads.

Sites can be paid for by charging directly for access, or funding through alternate means like Patreon. Content on the web doesn't have to be funded through the web, after all, plenty of people run sites on shared servers that don't make money. A lot of Youtubers are running sponsored ads directly in their videos because of Youtube's demonetization attempts. There are bound to be numerous alternatives to direct advertising that might be more acceptable to the end user, but we might also have to accept that most content on the web doesn't bring the end user value worth paying for.