Why would it be impossible for the President to "nominate" his cabinet prior to his election? All presidents have begun the nomination process prior to their inauguration, even though they cannot formally nominate them until they are in actual fact president instead of "President-elect."
In the British Parliamentary system, both parties go into the election with Cabinet Ministers already named. Thus the election is not man against man, but team against team. Which team do you want to lead the nation?
I believe this would be an improvement on our current system of buying a pig in a poke.