How is the First Amendment in any way related to YouTube?
Freedom of expression is relevant to Youtube because Youtube is a platform for expression.
If you don't like the rules of YouTube, go elsewhere. The true spirit of the First Amendment is that you have the right and freedom to do so.
Freedom of speech/expression is only freedom from the restriction by the government.
Youtube can refuse to publish anything it wants to. Zero people have an inalienable right to publish on YouTube's private platform.
Obviously 1A doesn't apply as-is, but maybe some equivalent should be implemented that does. At the same time, I'm not sure that's entirely fair since they aren't publicly funded. Or maybe it is still fair, or maybe there's some reasonable middle ground.