Maybe they are not regulating radio receiver usage, but the just the possession of it, which would be a separate kind of regulatory space.
All efficient radio receivers....
It is possible to build radio receivers without such. I built a crystal set as a child that could power an air piece without a battery using only the AM signal.
The police even have radar detector detectors.
I'm no RF guy, so I'm clueless on this stuff. But my understanding is that SDRs aren't radio receivers in the traditional sense. That's the whole "SD" part of it, the device scoops up everything and FFTs it or something.
A modern radar gun operates in the Ka-band, Google says between 33.4 and 36 GHz. Assuming 12 bit samples, your proposed solution needs to process a minimum 3.9 gigabits per second, or ~500 megabytes per second. To do this work in software would require a workstation.
Not to mention I'm not even sure if you can operate most ADCs above the 1st Nyquist zone like would be needed here.
These days hardware capable of that throughput can be had for less than $500 and draws less than 50W. 3.9 gigabits really isn't all that much by modern standards.
But they are suffering from the chip shortage. I was interested in using it as an X-band and K-band capable SDR receiver, which is a supported use case according to their media. But we'll see when it ships.
There are Radar Detectors that have VG-2 (Radar detector detector) detectors on them.
I haven't heard of a radar detector detector detector detector. Such a thing would be pretty useless for a cop's intent and purposes.