Even easier: Obviously there will have to be a "gun reprogramming device" which assigns ID chip numbers to specific guns, so as to "match" an issued firearm with the "authorized" user. This device will have to be employed every time a new "smart" gun is sold, or assigned to a different officer, or changes hands due to a sale, etc.
So how long do you think before one of these devices ends up in the hands of an unscrupulous someone who will happily "reassign" any gun to a new owner for a few bucks, no questions asked? All it takes is a crooked police officer to make sure that the device "goes missing" (or do the reassignments himself for extra cash), or someone to steal one, or anything less than an ironclad authentication system from the manufacturer (i.e. someone with a fake police ID might be able to order one through the mail, etc.). And if this technology wasn't just "cop only", every FFL in the country would probably have one -- not all of whom are honest.
And then there's the issue of computer hackers "cloning" the technology and then cranking out illicit copies by the hundred.
It wouldn't take long before there would be a willing "gun reassigner" for a small fee for any criminal who had a freshly stolen gun he wanted to make use of.