Your comment seems to make the assumption that this is a technical problem. You're right that it'd be possible to make a YouTube site by oneself. If one did it with GCP they could be using the exact same hardware and very similar software as YouTube.

However, the real problem the parent talks about is financial. YouTube gets all this hosting at cost for Google. A YouTube competitor has to pay the AWS, GCP, etc. markups. They'd also have significantly less advertising income than Google. Plus, many of the professional content creators wouldn't even consider a platform that doesn't pay out ad revenue.

That's the internet, it's just computers connected together and each computer belongs to someone. The more you have, the more traffic you have. The only way I can see this working is if the internet or parts of the internet become a public asset, a national cloud (like roads etc) paid by income taxes. Your videos would be on this public storage, common services would work like AWS services etc. It will be hard since this means additional taxes but at least the government will not be interested in competition (in theory).

Valid point, without money to burn it's not possible in any market.