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The answer is simply that QAM is very sensitive to phase error, and a frequency mismatch between the TX and RX radios is equivalent to a constantly increasing phase error. (Remember freq = change phase over change time) An IQ constellation of a QAM signal which has no PLL for carrier recovery will likely look like concentric circles.

In the ideal world, carrier recovery would not be required because the exact frequency used to modulate a signal would be used to demodulate the signal and no phase error would exist. However, in real world communications there are many factors that introduce frequency mismatches. Some examples include doppler frequency shift (resulting from moving objects), Tx or Rx LO frequency offsets, or A/D sampling rate offsets.

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Q: Why is carrier recovery required in QAM demodulation?
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