You can already do that thought not with a "Video tag." You can put videos on your server and have a Flash/Silverlight/Whatever player embedded in your web pages, It just happens that YouTube made this process very easy and became popular, in the beginning many people didn't even know you could watch videos on the web.
Anyway, I am waiting for the focus to get off of YouTube and for people to start realizing videos can be posted to many places, not just those that only allow 10 minutes and so forth.
What is needed is a standardised video tag like HTML, ported to all browsers, so people can host their own videos.
See a video as a HTML document or a GIF image.
I look forward to a W3C video standard crushing YouTube.