As a former poli sci PhD student, I'd like to add to this discussion. In my experience as both a poli sci undergrad and grad, the difference between undergraduate political science and graduate/PhD political science is so great that, pratically speaking, the two are entirely different fields. At the undergrad level, poli sci is basically a mix of history, philosophy, and current events. Some institutions include a token course in "methodology" which is basically introductory statistics, but by and large quantitative training is entirely absent. In contrast, poli sci at the grad/PhD level is dominated by quantitative methods and formal theories. It bears zero resemblance to undergrad poli sci. To be successful in poli sci, a grad student is better off having undergrad training in economics, mathematics, and/or computer science.
I asked one of my grad school profs why undergrad poli sci programs tend to avoid quant, and his response basically boiled down to this: Many (if not most) poli sci undergrads are actually interested in law, education, or "politics" (not poli sci) as career fields, so were departments to add quant training at the undergrad level, they would lose lots of math-averse undergrads to the other social sciences and the humanities. Fewer undergrads = less funding = less influence/prestige.