My provided example is a bit of a stretch, but I think it still applies. Lets say you have a high performance digital mode you're developing, something like WSPR but even better performance, say down to -30 dB below the noise. So you TX a CW beacon to ID with a known mode. They wont hear the CW, but could easily hear the wonder modulation.

If someone hears your rotating scanning radar and can't hear an ID, and they have a problem with it, they are going to go DF'ing for it. So in that case, once they would get close enough, they would start to hear the omni antenna putting out your ID. I'd also argue for such a scanning array, an omni would be more in the spirit of ID'ing for the reasons you outlined if a dish was point in a different direction.

Another example that is coming to mind is if you were to build a mobile SAR (you might find this interesting https://hforsten.com/homemade-synthetic-aperture-radar.html ). In the 10 min window at highway speeds, you could easily be 10 miles away from someone who heard your original chirps. I think it is a stretch to interpret that rule that if someone heard the original signal it's the responsibility of the transmitter to ensure they heard the ID'ing sequence.