The Oligarchs appoint the PeeM so that he can take care of their business and allow them to make obscene amounts of money in quiet and peace. Oligarchs like Kwas, Lees, Wees, etc don't care to approve the next PeeM. They only care that the Lee family who fronts for them will take care of this aspect. eg. when GCT was appointed as PeeM, they never needed to approve him because they know he was put in place by their man LKY, and hence will make sure business continues as usual. The next PeeM appointed by Gay Loong will also look after their interest. So, no need to approve.