In the British parliamentary system, the Prime Minister generally represents the office and the party first -- his personality is secondary. Harold Wilson, for example, is a very proper representative of the Labour party. He is its leader, but he is not an incarnation of the party.
The United States, on the other hand, developed a cult of the person in the presidency. This was true of Franklin Roosevelt and later of John Kennedy and Lyndon Johnson. Many Americans seemed to accept the idea that the President was bigger than life and somehow embodied his party or even his country. This concept was built into presidential operations.
The cult of the person, or at least the excesses of it, can be dangerous. It must be kept within reasonable bounds. When issues are so complicated that the people have great difficulty sorting them out, they may decide to trust someone who seems to have some answers -- or at least knows the right questions. But the danger is what the Germans proceeded to do when they decided to trust Adolf Hitler. I am not implying that we have reached that point; fortunately, we are still in an area where things can be sorted out and debated.
But the danger is there and must be kept in mind, especially during presidential campaigns. Many people seem to look for a hero, almost a deity, in their candidate. The Greek poet George Sefĕris wrote a poem that bears on this point. He told of a mule that slipped while carrying the Queen. The Queen fell, broke her neck, and died. Soon after, the spirit of the Queen appeared to the mule-handler and said, "Do not punish the mule. For I was full of the will of God, and that was too much of a burden for any beast to bear."