I don't dislike the idea. But, that too would be an injustice. We are not a nation of one gender. I think better options would be:

Increase the number of justices to 21 or 25 permanent seats. For the first increase, give the appointments to the parties, with the party in power having a 1 justice majority. Thereafter, return to the system of a POTUS appointing nominees.

Codify that the Senate cannot limit a President's length time left in office in which to appoint nominees.

Institute term limits. No position in a democracy should be a lifetime position.

Require stricter standards of judicial records. In other words, require a minimum standard of argued cases before a court and a minmum number of years sitting on a federal court bench, and a national professional certification standard before a judge may be considered for the SCOTUS. If a reliable professional organization like the Bar Assoiciation says that person is not qualified, that person should never come up before a nomination committe in Congress.