Problem is that requires good faith from both sides. If only one side adheres to that then the other side uses it as ammunition and inputs their politically appointed judges anyway.
Case in point, Senator Mitch McConnell crying out in 2015 about Obama wanting to appoint someone at the end of his term, saying that he would be robbing the next president of that legacy and it would be a political appointment. And then Mitch McConnell said nothing as they appointed and Trump approved three blatantly political nominees.
Both sides have to agree that those positions be apolitical or one side just ends up getting screwed. And of course we are not going to see that because Republicans don’t have a shred of decency left and the whole party.
In theory that’s how it works already. In practice, there is currently no disadvantage to appointing partisan judges and no system in which to objectively measure partisanship of a candidate. What that means is that there will always be partisan parties appointing partisan judges and there will always be candidates who claimed to be neutral who will be either accused of or proven to be partisan anyway.
In the current system true neutrality on the bench does not exist