But why is the radiation not shielded by the computer? We have tons of regulation for this kind of stuff AND a metal body that should stop most of the signal.
Let me give you an example. non-industrial is not allowed to emmit more than 3V/m, but non industrial product are also not allowed to be disturbed by 3V/m. So far so good. This only applies to 'disturbances' or 'non use signals'. Let me explain:
Now, radio transmission is different (like a mobile phone). The use signal (which is not a disturbance) is allowed to be much higher, like 40V/m. (So there was a case where a coffee machine broke when putting the mobile on it). This is all in perfect compliance. (of course the manufacturer of the coffee machine hardened the device, but this was market forces).
So for the other direction, I am not too sure but it can perfectly fine that the allowed EMC disturbs the reception of a radio signal device. Also EMC is only tested in 'typical' situations.
About the legality by using Software to intentionally transmit signal (def not legal without HAM license or proper FCC testates) I have no idea who would be the liable party i n this case.
Engineering circuits to reduce EM is actually very difficult, and gets more difficult as you desire less radiation. The regulations are generally about “harmful” interference and being detectable over a short distance isn’t that.
There are regulations, but they don't mandate perfect attenuation. They only specify that your emissions shouldn't interfere with licensed users. Since the licensed users are pretty far away from your computer and the power is very low, it's generally not a problem.
(As for sensitivity, remember that GPS signals have a power of something like 10^-16 watts at the surface of the earth, and you can receive those just fine. Radios are very sensitive instruments!)