That may be true. But I also think that our system for selecting scientists may filter out those who would like to go into politics. A lot of people go to law

That may be true. But I also think that our system for selecting scientists may filter out those who would like to go into politics. A lot of people go to law school who don't really want to be lawyers. They claim they're going to law school to "learn to think". Elite law schools are easy enough that people who aren't completely devoted to the law can still graduate in fine standing in three years with a few hours a day of study - so the system can still work for people with a more diverse set of interests and goals. PhD programs in STEM fields programs are very different. They are all consuming, and you need to be capable of focusing deeply on narrow research interest for years. Another thing to keep in mind is that a very high percentage of STEM PhDs in the US are international students, which may lower the interest in entering politics somewhat. There are other approaches that could work - maybe MS degrees, or a more professional degree approach to science doctorates. Lastly, there just seems to be a cultural notion - humanities and law are considered "broad, well rounded" educations, whereas science and math is considered narrow and technical. This is completely wrong, but it's a sticky notion.