That they study philosophies (what philosophers do) is important. They need to know how people think, and what their own philosophy is. Soviet premiers studied philosophy. The Mullahs study philosophy. (I won't bring up Hitler) The mere act of studying philosophy is important, but not paramount. Good leaders must HAVE GOOD philosophies.
A growing trend is the 'take charge' kind of leader who dashes ahead all glory and idealism without any practical backup. This often leads to a staggering disappointment and discontent in the populous when the election day promises fall by the wayside. What we need to see more of are people who study history, humans in general and societies. People who remain realistic and attuned to the common man and woman and who can push through with common sense, quality of life adjustments in a stead manner instead of launching half-finished and unsatisfactory attempts.
In today's governments worldwide we have far too many idealist politicians who spew bogus party line ideals and never follow through on the actions associated with them. To have a better city state today we need real hands-on leaders who lead by example and acts, not by philosophy. The early times where governments and forms of government are constantly evolving have gone. We have the types of government, we have the parties, we need those who lead by example.