An AOC is definately not overkill. Without it commercial air transport would be undercut by unscrupulous operators undermining safety and service, the result would be a very dangerous scenario indeed. It would be very naive to imagine that self regulation would suffice in a dog eat dog open market such as biz jet operations.
Private operations on the other hand do not have the direct competition that would lead to this downward spiral.
The regulations are vital, they just need to differentiate between what are AOC operations and private, non commercial air transport operations.