I could list just a few off the top of my head. Like Gohmert.

Really? I think as poorly of Louis Gohmert as the next guy - he's a genuine doofus - but he's a college graduate, admitted to and received a degree from Baylor Law School (which is a fairly well-regarded school), etc. Even otherwise smart people can believe genuinely dumb things (hi, Sidney Powell! Or James Watson, for that matter!), or be phenomenally off-base in some regards. But a true dumb person is rarely going to do well in politics.

Politics is mostly a popularity contest. You say what people want to hear, you win.

How do you know what people want to hear? How do you say it in a way that works? How do you navigate the fact that "the people" is a plural, and many of them want to hear different things - sometimes mutually exclusive things? How do you shape what people want to hear, or which of things they want to hear about they will decide are important? Etc.?

A con man will tell people exactly what they want to hear as well - and you'll notice that popular depictions of con men usually portray them as smart. Because it takes a certain amount of intelligence to be able to read a mark, figure out what will work on them, and tell them what they want to hear. It's not easy, and it's usually not something a dumb person can do.