I think the presidency has to be counter-majoritarian, simply because I think the natural tendency is for power to concentrate into the hands of one man.
We developed an imperial presidency because in a time of crisis, it is easier for one man to take action than it is for a committee. But there is always a crisis that needs a strong central figure to combat. First it was the Great War, then the Great Depression, then it was World War Two and the Cold War and then Islamic Terror. In the future, the crisis will be the Cartels or the Debt crisis. Power will continue to concentrate until all American politics are devoted to four-year cycles of struggle to take command of the Presidency, followed by campaigns to undermine the guy in the office until you can get your man in there.
Sounds like the America of today? What comes after is worse, I assure you.
I think that keeping the office of the presidency counter-majoritarian incentivizes people to devolve power back to the Congress, or at least puts the brakes on turning the presidency into an elected dictatorship.