I agree. I have been avoiding them since a nasty fracas where they wouldn't rent my reserved car to me without the credit card that I had used to reserve the car (even though I presented valid ID.) Trying to rent another car on the spot resulted in an atrocious quote, all while trying to talk to some guy on a screen instead of a real person behind the counter.
Perhaps there is non-destructive way to remove power entirely?
Automobiles are equipped with fuse panels. Removing (then, presumably, replacing before returning the vehicle) the proper fuse would be non-destructive, and if this device is properly integrated, would do what you want. However, I wouldn't be surprised to find that this device is actually wired into the radio circuit, so in order to turn it off you'll have to forgo listening to music.
It's also possible that the contract you sign with Hertz forbids removing a fuse for this purpose. IANAL but that would be shitty. To completely CYA, it might be better to remove the fuse, intentionally burn it out by shorting across the battery posts, then return the burned-out fuse to the panel. Then you could plausibly claim "hey the device just stopped working".
IANAL, but I have worked on surveillance software. As far as I understand it would be virtually impossible for them to legally have a microphone running without you explicitly activating it. Signing the rental agreement is not explicit enough since other people could be traveling in the car and the definition of "consent" varies significantly between jurisdictions.
Perhaps there is non-destructive way to remove power entirely?