Ask HN: Why is it impossible to watch online videos anonymously?

I've used Tor off and on for a few years. I like the idea of privacy, but I consider the experience fundamentally broken if I can't watch any videos at all, which is the impression I get from reading around.

I don't understand why it is possible to receive HTML and CSS files anonymously but the same is not true of video files. I gather that it is the "plugins" but most videos these days support HTML5 players that are built into the browser. I would have thought you could simply fix the video player in Firefox to not leak PII. I obviously don't "get it." Anybody understand this?

(And if I've missed it in my searching, is there some alternative to the TOR browser that works more like a regular browser in letting you use the web, at least with regard to videos?)