This is what happens (in theory) with GSM mobile phones. GSM devices have a serial number in the form of an IMEI which can be blacklisted from networks if stolen [0]. There are, of course, still ways round it as detailed in the wikipedia entry - e.g. the blacklists are national ones, and organised groups can "just" ship the phones to another country and sell them there.

Even so, as you intimate, it does make it _harder_ to resell stolen phones.

[0] https://en.wikipedia.org/wiki/International_Mobile_Equipment...