Pokemon Showdown is a battling simulator first and and foremost. Graphics and visuals are not as important to Smogon because that's not the point. It's supposed to be used to allow people to battle without needing to own a game or needing to breed so many competitive Pokemon which is exhausting if you are just trying out something experimental. The battle simulation is first, no story, grinding (except for rank I suppose), no need for flashy graphics, or super long move animations. That's why its presentation is so barebones. They only need essential graphics such as the Pokemon models, health bar, etc. One could argue you could do away with that as well and just have everything in text format.
Though I suppose freezing the animation might not be too complicated, but considering freeze is so rare in showdown they probably didn't think about it.
