Yes a cop can run your license plate for no reason other than to check the plate to ensure it fits the cars description or if they are looking for a vehicle that fits the description.
Cops usually do not just run license plates unless they pull you over and then they run the license plate to make sure that the registration is good and that the license plate goes to that car.
Some people switch license plates on vehicles and so they want to make sure that the license plate is good.
If your license plate is good and it's registered in your name and it's the correct license plate for the vehicle then you have nothing to worry about.
The cops or police can run my license plates all day if they want too because I have nothing to hide.
I rarely get pulled over either and if I do I have nothing to hide.