Two economists have come together to research the question of whether or not countries are smart enough to put economists in charge of everything. Their surprising conclusion: Nope, not really! There are hardly any economist prime ministers and surprisingly not that many economist central bankers, at least if we're talking PhD economists and not "guys who took an Econ class once."
At Ezra Klein's WonkBlog, Brad Plumer summarizes the study and asks, "why aren't more countries run by economists?" Here's why: Because everyone hates economists. Economists are the worst. They're usually very convinced of their own genius, though. And they act like because they use math, their "science" is more sciencey than sociology or whatever, but it is still mostly just a bunch of made-up stuff. If a bunch of economists had been running the world prior to the 2008 financial crisis the 2008 financial crisis would not have been averted because almost no one predicted it.
But the most important reason there aren't a ton of economist prime ministers is that economists disdain politics. Economists tend to get a great deal of pleasure out of loudly attacking very popular policies (higher minimum wage! tax code giveaways to the upper-middle-class!) and they generally talk about normal people as little mindless "economic units" or something awful and dehumanizing like that. Economists don't want to "campaign" and convince people to vote for them, they just want to be appointed to positions of power by people who actually did shake a bunch of hands and tell people what they wanted to hear. An economist doesn't want to be an elected official who answers to voters, because that sucks.
Conveniently, the researchers did not bother to answer the question of whether countries that put economists in charge of stuff actually have better economic outcomes. But the economist in charge of Europe's central bank is currently purposefully imposing disastrous austerity on a bunch of countries that did not elect him, so really if you want to know why we don't let economists run stuff look at Spain's youth unemployment rate.