Takes2: No one disagrees that it is a machlokes haposkim, with great names on both sides, whether women may drive.
ghdora: The Mechaber didn’t give this Psak “over a thousand years ago.” And Klal Yisroel has accepted the Psakim of the Mechaber given in the S”A as binding. Furthermore, this Psak comes directly from Chazal. And even moreso, no one, that’s right no one – not before the Mechaber and not since the Mechaber, argues against this Psak in S”A (that’s also in the Rambam.)