Unfortunately for the human race, scientists recoil with disgust from politics
It's quite common for scientists to run for political office in some countries - Germany, Singapore, and China, for example. And it's hardly unknown in most industrialized democracies. Margaret Thatcher had a chemistry degree. Herbert Hoover was an engineer.
The relative scarcity of scientists in many political contests could have any number of explanations. "Recoil[ing] with disgust" is a rather far-fetched one. Care to provide any evidence to support it?
Nor are scientists in government a panacea.
After the 2015 elections in the UK, there were 26 MPs with science degrees. Remember all the great scientifically-inspired legislation they proposed? Neither do I.
The 2018 US midterm elections brought us to a whopping 18 "scientists" (for some definition thereof) to Congress. I haven't heard a lot of agitating for evidence-based policy or scientific methodologies from them since January.
Scientists are very capable of being wildly, irrationally, fixedly wrong about things - important things. Take Linus Pauling's obsession with megavitamin therapy, for example. James Watson's racism. Freeman Dyson's metaphysics and global-warming denialism (which he admits has little or nothing to do with actual science, but is based purely on a visceral reaction). Michio Kaku is a loon when the subject of nuclear fission power comes up, and he's kind of wacky on UFOs, too. Want an example of an actual politician with real scientific credentials but patently stupid behavior in office? I give you Ben Carson.
Scientists, particularly the attention-seeking sort who are likely to find political life amenable, seem to be prone to ultracrepidarianism. Perhaps not moreso than the typical politician, but they often seem capable of a peculiar sort of double-consciousness, in which they believe they're still applying the protocols of scientific epistemology, and so they can appeal to its authority, but in fact they're abandoning not only scientific method but for the most part rational thinking, when they step outside their field of expertise.
It's certainly possible that democratically-appointed republics like the US and UK would, on the whole, do better if their legislatures and other elected offices were occupied primarily by technocrats who were trained in scientific methods and who insisted on applying those methods as much as was feasible, and who also acknowledged the limits of their own expertise. Good luck finding a candidate pool matching that description, much less getting them elected.