Executive power vs. accountability

When comparing our form of democratic government to other types of government altogether, like the British parliamentary government, it is easy to see that each was picked for very different reasons, and that each has its own strengths and weaknesses.
I find the idea of the "Prime Minister's question time" very interesting and I would love for our president and perhaps higher cabinet members to have to come before an audience and justify their actions. I would love to see a mother who has lost her child to the war in Iraq be able to face our great and fearless leader and for him to have to explain to her why her child is dead, for him to have to face tears and grief in person. I think that people who are opposed to systems in our country and who have been wronged by them should be able to bring their concerns directly to man himself, and not just write to their congressperson and watch nothing change. I think that anyone should be able to question the people that make decisions high up in our government face to face, and be able to get answers.
But I would not trade our balance of power for it. The thought of one man being able to do just about anything with our country, as long as he was determined and willing to deal with the political consequences, is just terrifying