An <img> tag pointing to animated gif should work on every combination of image host + CMS + browser.
I'm not sure off the top of my head what HTML 5 market share is like (anyone with recent data want to chime in?), but I'm guessing lots of people are running browsers that still don't have <video> capability.
The percentage of users not able to use <video> is roughly equivalent to the percentage of users running IE8, which is about 20% right now, and probably will stay there in the near future, as XP users cannot upgrade to IE9 (thanks, MS!).
The other problem with <video> is that there is still no common format which every browser supports, so even if you would ignore IE8 (or provide a fallback via Flash) you'd still have to encode all videos twice (to H.264 and WebM/VP8).
Sad as it is, but Flash for video and animated GIF will stay with us for some years.
I'm not sure off the top of my head what HTML 5 market share is like (anyone with recent data want to chime in?), but I'm guessing lots of people are running browsers that still don't have <video> capability.