The main point here is that neither the government nor Apple could guarantee that this backdoor software would remain safe. If the FBI brought the phone to Apple to update the custom OS, the software would then exist, which is inherently a dangerous situation. Furthermore, suddenly a precedent is set wherein Apple is obliged to continue unlocking phones for the government with custom created software. I sincerely doubt any organizations involved would tolerate the continual creation and destruction(can data be truly destroyed?) of customized OS's each time the government needed access to a phone. That means, the incentive is to create and maintain this backdoored version of the OS, setting up the exact vulnerability Apple is trying to fend off.

Basically, this project, from whatever angle it is approached, has a non-zero chance of backfiring dramatically thus risking the security and privacy of millions of iPhone users throughout the world.