All technical problems with that idea aside - and trust me, there are many - I don't really think a moving trainer card would be as aesthetically pleasing as you'd think, what with the differing animation speeds of the Pokémon sprites and trainers (something very few sites have gotten right yet, by the way).
The thing is, if you look at where trainer cards end up being - in forum signatures, profiles, and other things like that - it can't be too obtrusive or it'd just be annoying. If we start irritating forum moderators, we'll suddenly find the trainer cards being unusable, and thus useless.