You are correct that there is no constitutional right to be able to post videos.
But if someone chooses to operate such a service, and establishes rules, they must also abide by their established rules, or at least have a reasonable basis for their actions.
It becomes a public space, just like (for instance) a restaurant. They can't refuse to serve you just because they don't want to, they must have an appropriate reason for their action.
You may not have any "right" to eat in a restaurant, but once the "public space" has been established, they must have valid reason not to serve you.
You Tube is a public space, not a private club.