alt Hacker NewsGP 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.