>Oh yes it is. The government in most (all?) developed countries has special (often at arms length) relationships with utilities, research institutions, nonprofits and NGOs, universities, etc.
Youtube is none of these things, it's private property. The government in free societies tends to respect private property. Especially when that property is a platform for speech. Television and radio being an exception because spectrum is a limited resource, but there is no equivalent to that on the internet. Youtube's dominance is not the end result of their control over infrastructure, we could have a million video platforms on the internet, if we wanted.
>This is probably the most extreme interpretation possible of what I'm saying. Do you really think it's what I'm suggesting?
I think it's the inevitable result of what you're suggesting. Why stop at Youtube, after all? Aren't Twitter and Facebook also "sufficiently important?" I've seen people suggest any social media platform with over some arbitrary number of users should be automatically nationalized. It's a moving target.
And of course, these platforms will be regulated and censored, because that's what government does.
Again, I think a better solution would be for governments (or even academic institutions) to create their own platforms. That would be more in the spirit of the internet, rather than centralization and government control.