Do regulations permit an airliner be equipped with a radio transmitter which cannot be controlled by the crew?
All equipment on board needs to be interruptable, either by direct control input (turning it off) or via circuit breaker. This especially holds true for equipment that is capable of broadcasting or emitting radio waves, such as radio telephony equipment or the transponder. 

If the transponder for any reason became damaged and started to send incorrect replies to ground interrogation, it needs to be shut off in order to not confuse ATC systems or other aircraft's TCAS. Electronic or electric systems also need to be shut down in case of eletrical fires or other safety hazards to the aircraft.