As for the senatorial "Advice and Consent" thing, recall that it was established before the 17th amendment was enacted. The Senate was originally intended as a means of representing the interests of the several (and "sovereign") states as states - not as a body representing the will or interests of "the people" (which is what the House of Representatives was supposed to be for).
IMO, when the Senate lost it's character as a "check" or "balance" for the use of the states against the feds, the whole point of "Advice and Consent" was effectively neutered. Indeed, the whole point of the Senate itself was effectively neutered. (Such neutering was the purpose of the 17th amendment, after all - blandishments to the effect of "muh will of the peepul!" to the contrary notwithstanding - given the much larger constituencies of senators relative to house reps, the Senate is even less "representative" of the "the people" than the House is.)
But to whatever extent (if any) that senatorial "Advice and Consent" ought still to apply to new executive-branch appointments, I can see no reason at all why it should also apply to executive-branch expulsions - especially when the "expulsee" is a holdover from a previous administration. At the very least, the Chief Executive should be permitted (or even expected) to fire any such executive-branch holdovers - at will, and for any reason.
What possible purpose is served by forcing a present administration to retain executive bureau appointees from previous administrations? Whose interests are served by such a scheme? It certainly isn't "the people" (or "the several states", even if that was still a going concern any more - which it isn't)? So who, then?