Why didn't Nixon ask JFK during the 1960 JFK debate "answer me JFK, will you, or will you not, pass civil rights legislation during your term as President?" As a way to further exacerbate the ever-growing north-south divide between Northern Dems and Southern Dems?

I know a lot of people say that Nixon really struggled with the 1960 debate, but I feel like Nixon could have won the debate against Kennedy in 30 seconds by just asking JFK whether or not he supported civil rights, because if JFK says "yes," the southern Democrats will defect from JFK and vote for the unpledged electors/Harry Byrd, but if JFK says "no," the Northern Democrats will just stay home, or vote for Nixon. Why didn't Nixon just ask JFK if he would support civil rights? Keep in mind that roughly 90% of Republicans supported civil rights and 10% opposed them, while 50% of Democrats supported civil rights while 50% of Democrats opposed them, so JFK would have a much more difficult time answering that question than Nixon.