Running the country as a MoC (Member of Congress) requires a different set of skills than running an agency. Presidents tend to either, IMO, look for Yes men (bad idea) who will simply do what he says, or they look for strong-minded leaders from the private or public sector (good idea).
They have to resign their Congressional seats because there isn't enough time to do both jobs and Congress has rules about them not being involved in other employment such as this, which would create an untenable conflict of interest with the way our system is set up. I know Winston Churchill wore many governmental hats simultaneously but he was an extraordinary individual and his type doesn't often surface.
Some Congress members have gone on to do a stellar job as Cabinet officials. John Ashcroft comes to mind.
I think in someways it would be better if our Ministers just ran their own departments and did not have to worry about their constituencies as well. How can a Prime Minister have time to sort out problems in Sedgely when he has a country to run or Brown worry about Scottish issues when he is Chancellor of the whole of the United Kingdom; there must be a conflict of interest at times and the bottom line is that their Constituents cannot be properly represented.