Yes, sadly phones with removable batteries seem to be antiques now.

There are still plenty of slightly-used phones with removable batteries that work quite well. Galaxy Note 3 and 4 (possibly 5?) for a start. I recently got a Moto E5 brand new and it too has a removable battery.

Not even then; many electronic devices (PCs, for example!) have coin-cell backup batterys or large capacitors to keep RTCs and the like running during a battery replacement (or mains power outage).

Since radio and gps use a lot of battery, I wonder if a coincell could really power them.

You don't actually need to transmit the data off a backup battery, just store it and ship it out once a proper power supply is reattached. (You lose the data if someone destroys their phone, but that's a much narrower range of scenarios than "turn it off, but for real".) I don't recall GPS recievers being particularly power-intensive, but there's plenty of other sensors to log, most notably the microphone.

You don't use your phone for navigation a lot do you? It drains the battery very quickly.

I mentioned radio, because wifi / cell tower triangulation can be used to infer location.