Self-hosting video content is either not very simple, or not very featureful.
You can put an html video tag and call it a day, but you'll be missing out on using the best codec for each viewer and bandwidth adaptation and (last I looked, hopefully I'm wrong) usable UI.
Bandwidth is an issue, although I've seen enough high bandwidth, unmetered server offers that I think it might work. Depending on where your viewers are and where you find cheap bandwidth, you might get poor performance just from distance, whereas YouTube and Facebook have CDNs with nodes everywhere.