That would be interesting to see, maybe even viable with less cubemaps. Unfortunate that you'd probably need the source engine source code to add such a capability. And then, it might not be desirable in all situations. Maybe you'd be able to set up cubemaps in hammer reference only specific cubemaps to interpolate with, similar to how multiple overlay faces can be selected.

It would be interesting to see how the reflections would look if someone was somehow able to make the cubemaps interpolate with each other

I think the cubemap reflection room works by cutting up the floor into 16x16 pieces and having many many env_cubemap assigned to each piece. That would have an absurd performance cost for a bigger map, would not recommend.
Why I think it was done like that: the way the reflections move (or don't) and looks pixelated, also when you put mat_wireframe 1/2/3 in the console you can see how the floor is cut up, finally with +mat_texture_list you can see the map has a huge amount of cubemaps