If you give voting power to the people they'll just choose someone with a nice face and smooth voice, telling its all gonna be ok.
Unfortunately most of them come from the first category :/
Just as a matter of interest - the current Czech prime minister, who, at least in theory, has more power than the president, has graduated in physics, and has actually worked in research for some time. Angela Merkel (coming from Eastern Germany) has also a scientific background (in physics and chemistry).
But otherwise, it seems you are right about the fact that there is no such rule about post-totalitarian leaders being educated in engineering or sciences in general.
Btw, the rest of the Eastern European countries can learn a lot of things from the Czechs.