The US is weird in that a lot of commonly expected services aren't supplied by the government, if there was a wewillhostyourvideos.gov site out there then I'd definitely agree with you - I still _mostly_ agree with you since youtube now has semi-legitimate competition from vimeo - vimeo fails hard as a browsing platform but is fine as a place to host your video.
This sort of censorship by a private company is only acceptable if there is a legitimate other path to post videos (still within the realm of ethically decided censorship) - if the government has a presence in a market we demand that the government be the most lax player when it comes to issues of freedom of speech, but I think we're fine as long as there exist places in which to practice our free speech.
Is there any government in the world providing a wewillhostyourvideos.gov? More to the point, video is not the only form of speech, web pages exist, podcasts exist, I am not sure why freedom of speech now equals video and why people insist that the ability to post video to a privately owned platform is now a right just because that platform happens to be popular.
I am unaware of any governments that provide wewillhostyourvideos.gov, as to the question of mediums... it's a delicate balance. It is very logical that the government doesn't need to support everyone's ability to paint their opinions on a forty foot canvas with premium oil paints, but I think video based (and even more specifically that vlog/video essay form that has emerged recently) is a way that people feel naturally suites their self expression, if it isn't heinously expensive to support them expressing in that manner then I think we (as a society) benefit a lot from supporting their expression in that form.
This sort of censorship by a private company is only acceptable if there is a legitimate other path to post videos (still within the realm of ethically decided censorship) - if the government has a presence in a market we demand that the government be the most lax player when it comes to issues of freedom of speech, but I think we're fine as long as there exist places in which to practice our free speech.