I generally use a Closer, but he's not my best RP or even my second best. Bear with me, this is probably classic overthinking.
I'm one of those who believe the modern "save" is light work. Ninth inning, just get three outs without a run scoring (or one, or even two.) And the pitcher might even be facing a weak part of the order. In those cases I'd rather not use my best RP in which case then he'd then be gassed for the next game.
So my closers are usually guys with obvious weaknesses. Lower control, DUR/STA combo, or only one good pitch. Guys who aren't actually as good as my real SuAs. My best guys pitch the 7th and 8th innings.