Re: I think it's a reasonable idea.
The last time I poked my head into the Comcast Arris cable-modem/router, I noticed it has recorded the MAC address for each device if it's ever connected. The accuracy is, of course, limited if any devices MAC addresses have been (randomly) changed. I'll give you three guesses to pick whose devices do that regularly, but you'll only need one. [Blowback minimization again.]
So, if a device has been stolen, logs in your network devices can be your friend.