Because it protects the republicans from the mid-term election fallout: If in open session, they take it easy on her, don't challenge the veracity of her charges/memory, it hurts Judge K. and will piss off the conservative base. If they take her to task, the women vote democrat in the November mid-terms. Any senator after the hearing that votes for Kavanaugh will then be blackmailed/threatened politically and/or physically.
Even if it’s closed-door, Feinstein or one of the other Senators will leak the transcript like she did with the full transcript of Glenn Simpson’s closed-door testimony. There is no protection for Republicans whether it’s closed or not.