Nice! Is there any slowdown it is hard to say from the video?
I haven't run the profile on this, but qualitatively, no noticeable performance hit. I'm using 1024 px^2 for each cube face, which might not be optimal on all platforms/hardware configs.
Also, I haven't totally figured out the question of when to update the reflection probe. If nothing is changing, then it is overkill to update every from or even on a fixed update loop. Also, you might just want to have this in the editor and bake the probe to a texture on disk...For now, I've just implemented an Update() function that I have tied in to my specific use case.
I was thinking of doing a PR for this - would it be useful to anyone else?