Michelle Obama was on once, IDK why a president never has been. Would have been funny if HW voiced himself in the episode where they skewer the crap out of him.
I believe Angela Bassett did Michelle's voice
Huh, this is like a Mandela Effect thing to me cause I could have sworn reading somewhere that she voiced herself. Oh well, guess in that case no POTUS or FLOTUS has ever been on the show.
As for my best guess why no American politicians has ever seemed to want to go on the show? Well, back in the day, it actually had a reputation as being a bit edgy and controversial, tame as it seems now. So they might have wanted to avoid association with it and any controversy that might have gone along with that. Plus they probably would have had to make fun of themselves, and politicians tend to have egos that might make them not like that. Though some have more senses of humor than others, and they tend to be self-deprecating at the WHCD, before Trump anyway, who obviously has the biggest ego of all. And hell, Hillary Clinton went on Howard Stern! (Though not until after her career was over.)
They might, of course, just not like or care about the show, especially nowadays. When it was relevant, it was controversial, and now that it's not so controversial, it's not relevant. So maybe the timing was just never right.
This Wiki article has a long list of all the guest stars that rejected the show or didn't pan out, and it includes a number of politicians, including POTUSes and VPs. Apparently Reagan was actually the only one of several presidents who responded at all to their request for one episode.
There's also a whole backstory to the episode they did which revolved entirely around George H.W. Bush, which I know because I own all the early seasons of The Simpsons on DVD and used to watch them all the time. The disc with that episode had a featurette which showed how Bush once bashed the show in a speech, saying the country should be "more like The Waltons and less like The Simpsons." The writers subsequently wrote a letter to Barbara Bush in-character as Marge, and she actually responded favorably. But still, they made the episode making fun of them as a result of all this, though Barbara gets off pretty lightly while George is mocked mercilessly.
