A banal observation: everyone is assuming that the radio speaker is disabled while I transmit (or that I use an earpiece that the microphone can't overhear. I'm guessing the first is actually the case with handheld radios.

It can be difficult to pretend to be unable to hear someone on the other end of a two way communication. The impulse not to interrupt is strong enough to cause detectable irregularities in speech. Actually breaking, or at least turning off, the receive capability might be essential to maintaining the impression on the other end that it's broken.

It is difficult to consciously pretend. That's why our brains don't leave this particular gambit up to our consciousness. It does seem that this, as you say, involves genuinely breaking the receive capability, but evidently the actual cost in terms of information wasted is worth the price.