Afaik, on pretty much every modern car the single main antenna unit (usually the shark fin on the roof) handles cellular and GPS (Rx only) and radio (AM/FM, and often also weather/traffic, Rx only).

So you'll lose the other things if you put it in a Faraday cage.

A cage is a bad way to do it anyway. It's easier to disconnect the cable between the antenna & the telematics module (which has the SIM and control electronics in it). Or disconnect the power to the telematics module. Etc. Depending on the wiring harness style and design of the car's electronics, that may also let you disconnect just the cellular antenna while leaving the GPS/radio antennas connected.

In the future we might see those components getting integrated together... But you can always physically destroy/remove the antenna.

Its all very interesting as an idea. But in reality when things go fully tracked you'll be fined for not having location data for every trip. It will impact insurance. Your registration. Even basic road usage. People have this idea right now that public roads will always stay free. This is not guaranteed.

Even the coming road taxes are all about constant tracking. How far / which road did you drive? They'll demand the answer. And you put a faraday cage to stop this? Suspicious. The default assumption is going to be fraud. Criminal behavior.

All the EVs will soon enough have some variety of tracking sooner or later. So thats basically all new vehicles. The alternatives will also, whatever they are. Hydrogen?

Transport privacy is likely dead already.

Sitting next to an internal combustion engine in a mostly-metal box is already pretty noisy as RF environments go. It's much easier to find and disable the antenna than to try to shield it off.