Trump would be a fool not to make a Supreme Court appointment, of course, and he has done it, but the executive branch is co-equal and doesn't have an obligation to comply with the act of Congress from 150 years ago by appointing a replacement for RBG to make it nine if it doesn't want to make an appointment for prudential or even political reasons.
The executive can say the court costs too much and for that reason not make the appointment. The executive can say the court hears too few cases to require a ninth justice. The executive can say "eight is enough". Marbury v Madison, perhaps the most consequential decision ever, was decided by a Supreme Court 4-0 with a 6-member court (two were sick at the time). There was no magic odd-numbered formula which was required before that decision was made. No one today as a matter of politics views the decision as illegitimate for that reason, nor because the case was decided by too few members.
And FDR certainly is precedent for saying there were prudential reasons for believing the nine member court was inadequate for the historical moment. Just because he lost in this political quest doesn't mean it was illegitimate.
Consider that FDR wanted to pack the court in 1937 through a bill scheming to swell its numbers because the Supreme Court kept thwarting his New Deal legislation in Congress as unconstitutional from 1933. The Great Depression was a dire moment in American history, requiring, in FDR's mind, one attempt after another to alleviate it, no matter how unprecedented.
The other powers that be thought otherwise.
But eventually and fortuitously one justice on the Supreme Court, named Roberts !!! by the way, actually switched sides to favor a New Deal case pleasing to FDR, which ended up having the odd result of taking the wind out of FDR's court-packing sails.
The March 1937 5-4 decision came to be known for this reason as "the switch in time which saved nine". The court showed that it could, in fact, rule New Deal ideas constitutional. That removed the argument for packing the court, by effect if not by intent. The nine member court was adequate after all.
It's an interesting case showing the power of the Supremes, not just to rule, but to maneuver.
The presidential appointment power is a political matter because the president is elected.
But don't kid yourself that the court absolutely eschews politics when rendering its opinions. Though not politically conservative in nature, a March 1937 ruling upholding innovative, New Deal legislation, ended up preserving the traditional character of the Supreme Court reaching back to just after the Civil War. And it persists to this day.
The founders were genius in this respect, recognizing that political forces are inescapable and must be accepted, accounted for, and balanced in order to prevent a lurch into the absolute tyranny of a single one of the branches of government.
The imperative of the moment is the free exercise of politics within the constitutional framework, not tampering with the framework.
