Why in the U.S. is the direct leadership of the President so important? This question should be taken in context of the Vietnam War.
The Vietnam War shows the importance of direct presidential leadership in a few ways.
First, the lack of such leadership caused problems for the United States at times. The American involvement in Vietnam escalated gradually, often without direct presidential involvement. It would have been better for the US if various presidents had been in more direct control because then there might have been a more coherent strategy with a defined goal. Instead, there was "mission creep" as the military gradually got more and more involved almost by accident.
Second, though, Vietnam shows how direct presidential involvement can be important, but bad. This can be seen in the Gulf of Tonkin Incident and the Congressional resolution that followed. There, Pres. Johnson used his direct leadership to formally push the US much farther into the war. He did so even though the provocation (the Incident) might not even have really happened. So, in that case, we see how much of an effect direct presidential involvement can have. Unfortunately, it was a bad effect.
So both the actions and inactions of presidents in the Vietnam War show us how important the direct leadership of the President is. It is important because only the President can set clear goals for our country. Otherwise, our efforts become confused and unfocused as military leaders or lower level officials set goals instead of having those goals set at the highest level.