Trick question, there shouldn't be SC justices. :)
But, since there are SC justices, no, the president should not pick them. It is only done when the president is lucky enough to have an open spot to fill, who knows when it will happen next and who will be president. At the very least congress should vote on them and they switch every several years or something. *That is kinda how it works now but I think the president should not be involved in the appointing process, where congress can only vote to reject him
RE: Is the Real Problem That President Select SCOTUS Justices?