I'm not so certain I agree. For one, I don't think corporations this large should be able to entirely subsidize entire mature businesses (and control them) period. That's the force they exert in the market that's anti-competitive. If an alternative isn't economically viable, than the business just isn't there.
Given the little I know about Facebook's server infrastructure, they don't really have the capability to deliver a "Baby Youtube" anytime soon. They don't have the physical space available for the hardware they'd need and if they did it would rapidly be absorbed by their larger teams who need it already. Plus they just don't do high quality video well. That combined with the visibility limitations of the feed don't really make it a great platform for self-branding, unless you're willing to shell out major cash for promotion.
Amazon makes more sense as Twitch is already a good analogue for Youtube. It also pairs well with their budding media empire. That said, Twitch actually brings in money -- it doesn't depend entirely on subsidy to function.
I think what I'm getting at, ultimately, is that hosting your own video content probably shouldn't be free. I'm sort of tonedeaf to complaints over the streaming Adpocalypse because these streamers/person-brands exist purely through advertising subsidy in the first place. If the quality of your content is good, it's worth paying for distribution (and/or self-hosting) because you will see a return.
So it turns out that Vimeo is probably the right choice. Reviewing their content guidelines, it seems as though most of the commercial content that has been kicked off other platforms fine as long as it isn't spammy or sexually explicit.