Was Qing army fragmentation deliberate?

Was the Chinese army kept disorganized because Chinese troops were also a threat to the ruling regime?

Largely yes; fear of concentrated military power helps explain why politically safer fragmentation survived despite its wartime cost.

Political control helped preserve a deliberately divided force. The older arrangement had once limited the danger of arming ethnic or provincial groups heavily enough to challenge the regime. China could still have combined selected Green Standard troops with the better Huai Army to form several useful field corps. That reform was administratively possible but politically dangerous because it would concentrate trained force under powerful commanders. A unified modern army could defend the state more effectively, yet it could also threaten the people who authorized and commanded it.