Besides, if you try to put a huge fan and compressor (rigid hub, no variable pitch) rotating at the N1 and N2 and N3 limit speeds in, say, ISA-65 Celsius conditions at Yakutsk or Yellowknife at -50 Celsius and sea level, the dense cold air propelled by the fan might, apart from pushing the plane off the runway in one-engine-out case, break something else. Like generate excess pressure in combustion chamber, or break pylon, wing etc. The engine, pylon and wing strength are fitted to the rated thrust - so if the air is denser than ISA+15, the fan and compressor must be slowed down to keep the thrust within what the engine can endure.
Do turbopropellers also have derate to prevent generation of excessive forces in cold and dense air?