"...Unless everyone in a country devoutly belongs to the same church, mixing religion and politics is a fools errand..."
That has certainly been the Western experience in recent centuries, although that was not always the case even in the West.
Throughout much of the rest of the world, however - including much of Latin America, Africa and the Muslim-dominated regions of the world, they haven't learned that lesson yet, to an extent that would preclude them from attempting to do just that.
And given that 90% of Egyptians are Muslim, with 10% Christian (mostly Coptics, presumably), their near-homogeneity of Religion gets their demographics in the ballpark of 'everyone devoutly belongs'... close enough to try, from time to time, apparently.
"...The hope should be that quality spiritual leaders are way to ******* busy to run a country."
Agreed... 'quality' or no... it seems to me that Religious Clerics, translated into power in a Secular State, almost always either (a) try to convert that State to a Theocratic one, or (b) screw-up the Secular State with their biases and questionable motivations.