The biggest issue I see is that those models (or rather their trained parameters) are usually pretty large (several GiB). So it'll take a while to set up in the browser before the evaluation can actually start. It'll also require a lot of bandwidth on both ends.
A lot of those things should already be doable with the fragment shaders we get from WebGL and a lot of hackery, like clever (ab)use of textures. So the actual issue that we're not seeing a lot of this is probably not due to it being impossible right now...