I think it works alright in times of peace and stability when difficult decisions do not need to be made, but in periods of conflict, chaos, or just national crisis it falls apart. Primarily because the proper course of action is usually a radical case, or when serious issues are needed to impose major changes, action needs to be taken quickly.
I think it's the latter case that warrants giving the president more power. It's a necessary evil. What has saved the United States a few times (Civil War and Second World War come to mind) was that we had fantastic leaders acting as president. Say foreign policy around 1940 was run by the vote of the people, or by Congress. The United States was isolationist to the core but Roosevelt made a daring and covert effort to prepare for war, and open dialogue with Churchill and begin Lend-Lease.