A lot of gyms have head coaches who are the owners/ part owners. The gym I work for is a bit different in that we have an owner (not overly involved) and a manager (who most people think is our owner). Under the manager, there are people in charge of each division (a main office employee, a head team coach, a head preschool teacher, a head birthday party instructor). This system works out really well for us.
I've read in some posts how if and when there is ever a problem, a lot of parents only have 1 person to discuss it with (the owner/ head coach), so whatever their decision is is usually final. Our system avoids this, it delegates work, and also encourages a lot of communication and working together because there are multiple people "in charge".