Couldn't they just use the QBZ-03, it can be used in 5.56 NATO?
They could in theory. However three factors.
first the QBZ03 hasn’t been seen in large numbers in the 5.56x45mm configuration. Though they exist the Norinco AR15 is more common.
second, as a competitive rifle the AR15 is unmatched. Its design lends its self due to the lighter recoils and highly ergonomic controls. Even a bone stock no frills AR15 is a far better competition or home defense weapon than most of its competitors.
Third as the AR15 type is perhaps the second most common modern rifle globally as a combat rifle and probably the most common rifle for competition, it’s far easier to get into competition. No questions on finicky safety rules. Most commercial accessory should fit for modifying as long as Norinco stays within spec.