If Charles Guiteau is remembered at all, it's as the crazy guy who assassinated a president because he wanted to be Ambassador to France. He thought President Garfield had promised him an ambassadorship, and he also thought God had told him to kill Garfield. He was delusional, no doubt about it. A lone nut. Just a crazy, crazy guy, is all.
What's less remembered, probably because it's too complicated, is that Guiteau's delusions were distorted and amplified by the overheated political battle between factions of Garfield's and Guiteau's own Republican Party. To boil things down so I don't have to write an entire essay explaining a forgotten old-timey political squabble fought by guys in giant muttonchops (if you want that, Sarah Vowell's Assassination Vacation is a fantastic read), Garfield was trying to dismantle the enormously powerful, enormously corrupt political machine in New York. The people running this system wanted to keep it going, because it made them what today would be billions of dollars--really, billions--so they formed a Republican faction called the Stalwarts to attack Garfield.
They really went at him. Accused him of treason, of disloyalty to his party and his country. Predicted the end of the republic if his reforms went through. Declared that he had to be stopped at any cost. Observed pointedly that Garfield's vice president, Chester A. Arthur, was a Stalwart in good standing. There was no TV or radio, of course, so they put out a lot of fliers and got a lot of editorials into newspapers. Blanketed the old-timey equivalent of the airwaves with ginned-up fear and politically convenient hate.
And so Charles Guiteau, who heard voices, who hallucinated that the President had promised him France, who would later, from prison, write a bizarre hymn to his own execution and wish aloud that he could have paid a little extra for a handgun with a mother-of-pearl handle because it would look prettier in a museum someday... so this lone nut, who undoubtedly had no understanding of or interest in the actual issues behind the Republican infighting, shouted to the horrified crowd as he was dragged away, "I am a Stalwart of the Stalwarts... Arthur is President now!"
And that's why we don't do that.
(If it makes you feel any better, the new President Arthur immediately turned on the Stalwarts and dismantled the old patronage system, which is why it's no longer common for large chunks of the nation's GDP to just vanish at the New York Port Authority, shortly after which all the government bureaucrats working in that neighborhood suddenly and mysteriously become multimillionaires.)