Discussion
What practical problem does a high crest factor cause in a transmitter?
Answer: A
It forces the amplifier to be operated well below its maximum output. The peaks must pass without clipping, so the mean power is set far below the amplifier's capability and the efficiency suffers accordingly, which matters enormously for battery life and for cooling. Multicarrier signals are the difficult case and a good deal of engineering goes into reducing their peaks. Bandwidth is a spectral property that the crest factor does not directly set, though clipping the peaks certainly does spread the spectrum. Synchronisation and antenna impedance are unrelated to the peak-to-mean ratio.
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