Well the vehicle checks are to check for a stolen vehicle. The cops would also cruise the local mall overnight and we ran any vehicles parked (the mall was notorious for stolen cars being dumped there)
Also, anyone arrested was run, but the reasoning for this is obvious.
My guess (again, I'm not LEO nor was I) is that there could be any reason to run someone that a LEO encountered, tho I know that not every person was run in the jurisdiction I worked in. (Now that the computers are in the cars, that may have changed.) I also know that the computers in the car, when they run a plate, run the registered owner through NCIC.