I have no personal problem with remaking The Cage - or any other episode of Trek. That said, it would make fans heads explode.
The basic problem is the almost religious nature that a lot of fandom has related to canon. I think arguments related to "visual canon" have been mostly defused, and the visuals could be updated without concern. But past this, you'd have to do one of two things.
1. Keep the original script almost in its entirety to not violate canon. The one exception to this might be adding additional scenes from a POV not seen in the original, since this would give the writers freedom to depict things we haven't seen before. An extreme version of this would be if the whole episode was reshot from the POV of Vina.
2. Just write a new episode that has the same broad strokes plot, but differs significantly in details, and tell the fan base that nope - the original Cage is actually not canon. Meaning not only visuals, but also scripted dialogue in Trek can't be trusted as something that really happened in universe.