One of the many reasons I use YT or Vimeo is that I simply upload the high-res render, edit some metadata and I'm done with a simple embed in most cases. Alternate versions for lower bandwidth are automatically made and automatically served, streaming is taking care of (YT really excels here), and there is a nice API to do interactive stuff.

I do use the <video> element from time to time, but only if I want to optimise the loading of an autoplaying video or there is some other technical reason.