How things are aren’t the only way things could be.
A receiver could use a new random ID to call “collect” to a secure third party network which agrees to pay for the base stations bandwidth for every connection. The station then responds to the base station yep ID X’s bandwidth will be paid by vert tel.
Obviously, this doesn’t eliminate the possibility of tracking as you’d want the cell to have multiple connections created and abandoned randomly, but it does remove that ID you’re concerned with.
GP is referring to manufacturing variance in the radio equipment, not the deliberately-inserted tracking identifiers. See, for example, doi:10.1016/j.dsp.2025.105201 and doi:10.3390/rs17152659 for relatively cheap approaches.
The solution to this is just to make it illegal to store and process the results of such analysis applied to radio signals, without consent of the data subject (GDPR jurisdictions have that already), and to enforce that law.
Intentional noise can obstruct that signal. Which should be obvious from a pure information theory perspective, if you can extract more information from a transmission to identify the radio a transmitter could modulate that to carry information.
Even going to the extreme of a friendly jammer producing a countersignal is only enough to fool the bottom end of hobbyists. The only thing you can do to stop SEI to a certainty is to trash a radio after you've used it once. It's an unsolvable problem outside of that, and known as such for decades.