When a police officer runs your license plate number through their computer they'll be able to pull up the owners name, address, license status, whether your license plate is current, and even possibly your photo from your drivers license.
The police officer can also usually tell whether your vehicle has current insurance on the vehicle and they can tell whether the license plate belongs to your vehicle or whether someone has stolen a license plate and placed it on a vehicle.
So stealing a license plate or putting on a different license plate will get you into trouble because if a police officer pulls up the license plate number and it is reported stolen or mismatched to the vehicle then you'll get pulled over and get into trouble.