There's probably too many places where embedding a full blown video isn't practical - at least not in existing products.
Avatars, emoticons, simple GUI elements (I'm thinking e.g. of a "copy file" dialog) and similar.
Don't forget that we now have javascript, CSS animations, canvas and webgl in addition to good old gifs to deal with animated features. Do we really need apng on top of that?
Little emoticon stuff makes more sense with GIF which are very inefficient with filesize but with very very little performance overhead.
This is just 'my gut' like you have said. A proper analysis of the performance of h.264/GIF vs resolution would be nice though.
I can think of one other hypothetical problem, although it would need testing to confirm: block sizes. h.264 works with block sizes that are a multiple of 4, and AFAIK codecs often perform sub-optimally with input that cuts off mid-block. For large videos that doesn't matter much, since you don't usually focus on the edge of a video, but for a small asset, it might be a problem. Someone with more knowledge of h.264 might be able to correct me on this.