I have childhood memories of picking up radio transmission on valve amplifiers - music amplifiers for guitars/keyboards
Lots of amps, especially the transportable mains record players, transistor and valve did pick up a passing taxi, ambulance, police or fire engine.
Nothing much to do with it being turned off, though I guess some valve amps might have had briefly "anode bend" detection. But I've been using, repairing and building valve amps from mid 1960s and I don't remember any worse at turn off. I added RF blocking filters (often a small coil and a capacitor) to many record players and amps in 1970s to cure them.
The Mobile 2 way radio users have moved to higher frequencies and also often digital which is one reason it's rarer. Also many amps now have explicit audio band low pass filter now because many CD players, phones, MP3 players etc output some RF (or 192kHz oversampling) on the audio out. That makes it rarer too.
But most powered PC speakers, powered phone speaker docks and TV sound bars are rubbish. You'll notice them buzz and warble loudly if phone is near, sometimes without a call, as occasionally the phone tells the base station where it is. If you don't want tracked, take the battery out. The phone HAS to occasionally listen for base and call it or else calling a mobile would need the call to go out on EVERY base station everywhere. This is why people can still phone you when you are in Germany or France on a phone normally in Ireland or England.
Your average 1950s table radio has a better loudspeaker than most phone docks, TV speakers, sound bars and small home theatre boxes. Plastic is rubbish for a speaker case. Decent bass is impossible on a small cabinet and as speaker size goes below 6" bass vanishes. A 4" speaker in an MDF box about 5" x 9" x 7" internal is about minimum. There is no flat screen TV at all with a usable built in speaker. The "bass" on modern small speakers is just a resonant thumping.
I have a licensed transmitter, on some bands it will come through clearly on PC speakers on the other side of the house.