Hey Tammy-san,
Anthro and history are definitely important when you are trying to understand why certain (environmental, social, economic) problems exist, but I think data-based training helps you deal with the "how."
As a policy-maker, if you have several different problems to address with what you're drafting, how do you prioritize which programs or regulations get attention/funding? You'll need to be able to go through data and draw conclusions. (Is carbon a more dangerous pollutant or is ___? Would it be more socially-beneficial to provide tax credits to struggling homeowners or to single-parent families? Does school performance increase when a school district puts more money in facility improvements as opposed to increasing teacher salaries?)
And after you put together a set of policies or programs, quant skills will help you measure their effectiveness. If in government, it helps you decide whether a program is worth expanding to other regions or agencies. If you're in a nonprofit, this information helps attract institutional donors who want hard numbers to help make their philanthropic decisions. (Cost-effectiveness is key.)
It helps to think of theory-based approaches as deductive, and data-heavy analysis as observation-heavy and, therefore, more inductive. You'll need both to become a good policy maker.