If someone breaks into my car and steals the car, then I'll know. Takes 2 seconds for me to go to my opener and wipe out all paired remotes. And then re-pair each car back into the opener.
If someone breaks into my car, and doesn't steal it but is looking in cubbies and glove boxes for something of value they will find nothing but my car registration as i never keep anything of value in any of our cars. The remote will not be anywhere in site and not in any cubbie or glove box. How would a criminal know where i hid my remote? Are they REALLY looking for that in the few minutes if that to take what they can and split?
Either way, i wipe out that remote and re-pair my remotes.