Lots of business leaders like to think that the top dog is exempt from the details of actually running things. It's a pleasant way to view leadership: you stand on the mountaintop, thinking strategically and attempting to inspire your people with visions, while managers to the grunt work. This way of thinking is a fallacy, one that creates immense damage.
An organization can execute only if the leader's heart and soul are immersed in the company. Leading is more than thinking big, or schmoozing with investors and lawmakers, although those are part of the job. The leader has to be engaged personally and deeply in the business. Execution requires a comprehensive understanding of a business, its people and it's environment.
The leader must be in charge of getting things done by running the the core processes -- picking other leaders, setting the strategic direction, and conducting operations.