I was a bit too sarcastic in my OP. I agree with you that someone with a background in what they administer is a boon.

But my point still stands. In almost all cases, the people vying for power positions are the wrong people for the job.

So the right person, someone that would be less influenced by power, needs to get chewed by their party and raise through the ranks. And if after all this ordeal, they still have their voice left in the party, then they make great minister.