Just my 2 cents, based on what we've all seen...
Yes, Rocco is indeed a chef, but is he a business owner first, chef second, or vice versa? Given he is more concerned with glad-handing and being in the front, as opposed to the back, I would argue he is playing owner first. Given the bottom line of the restaurant is to earn revenue (above cost if possible), Rocco's perception of the best use of his time is glad-handing, not cooking 300 meals per night. Emeril sure as heck does not cook every meal at his restaurants, so why should Rocco?
That said, we all see he is lacking in a few of the skills one might expect of someone who deals with the public. As I watch the show, I scream at the TV asking "where is the management of this place..the french guy, the floor mgr, whomever makes decisions?" Clearly, Rocco is too busy collecting publicity to worry about actually running the place, whether right or wrong. But he does have a GM, kitchen manager, floor mgr, etc all responsible for ensuring the operations run smoothly. Where are they?
Could be the editing, but all we ever see is people running to Rocco with issues he really should not be dealing with at the degree of detail he is. I am by no means saying Rocco is an angel here, but some of the blame lies in his subordinates (ie. GM and management team), who appear more concerned with identifying problems as opposed to providing solutions.