And the Rambam and SA codify that by saying that Chazal commanded us not to teach her.
Correct, but the fact remains that Chazal never said it’s assur; they were against it because of a bad result. Which is tantamount to saying that if this result will not happen then it would be ok to teach girls Torah. So at most there could be a machlokes in metzius if in our current circumstances, teaching girls will cause tiflus and if it will cause more tiflus than not teaching them.