The three judicial appointees can veto any selection, and are by far the most cohesive and only long-lived subgroup of that panel. In practice they run the show.
But if the judges veto, their power is, if anything, strengthened - it keeps the supreme court in their hands. I.e. they only share power with judges of their choice, or no-one. And they can easily wait-out short-term politicians and get the appointments they want with their successors.
Their power is strengthened as compared to simply choosing their own successors as was claimed? I'm not sure it is a great system, but America has stuff like the court packing scheme that this does seem to at least prevent.
