Someone would have to take responsibility for maintaining the list and ensuring it was correct. There would need to be a process for submitting the serial numbers of stolen computers, including verification that the serial numbers were valid and the computers were actually stolen....this would probably need to involve the police. If a serial number got on the list that was from a computer that wasn't stolen and somebody tried to sell it, who would shoulder the blame for the mistake ?
Maintaining databases sounds easy until you have to ensure that the records are complete and error free, with significant consequences if they're not.