Granted, it’s possible “Rick and Morty” will keep Curtis as the president throughout the show’s run. After all, like many animated sitcoms, the characters don’t really seem to age, keeping them in a form of stasis while commenting on new things happening in the real world. Curtis may always be the president, like how Richard Nixon somehow won more than two terms on “Futurama,” although he was pretty corrupt, so it’s not out of the question he changed Earth President rules.
However, assuming a presidential election does occur on “Rick and Morty” at some point, it’s easy to see a scenario where Rick (or a duplicate of him) would want to run. He’s constantly running afoul of the law and has to deal with the occasional annoyance from the government. Rick could bypass all that by putting himself in charge, and with his vast intellect, he would know precisely how to manipulate the population into voting for him. Once elected, he could do anything he wants (in the United States, at least) with virtual impunity.
It’s also possible Rick would want to be president just to mess with Curtis. Rick’s certainly not above pursuing the long con just to pettily get back at someone. If Curtis annoyed him one too many times, he may try to put him out of a job just because he can. Honestly, it would make for a pretty good story arc, complete with topical political satire. The show will need plenty more stories in the years to come, so “Rick and Morty” writers, consider this one a freebie.