As we know, Nixion's Head has been in office for quite some time, due to his argument of the rule "no body can serve more than two terms". Since he successfully became president, Why didn't other presidential heads run for presidency?
In 3012, Nixon tries to win over potential voters for another term by promising to build a fence around the solar system to keep out illegal immigrants. Nixon's only real competition was Senator Chris Travers, whom he tried to mud-sling by spreading rumors about him not being Earthican.
After Senator Travers' birth was broadcast on live television, more people voted for Travers, causing him to win the elections. By doing so, however, he created a paradox (as the only reason he came to the past was to stop Nixon's re-election) and he disappeared, leaving nothing to stand in the way between Nixon's fourth term in office.
That's one case. But I don't know why didn't other presidential heads run for presidency. Maybe Nixon's Head is put the law against other heads :)
Or maybe its creative thinking and parody to politics of Matt Groening. Like for example Mayor Quimby in The Simpsons.