WELCOME ABOARD!
If you go to your assigned patrol grid you get 100 renown. If you stay there 24 hours you get 500. You're supposed to get some for driving all the way home rather than teleporting, but reliable witnesses say this has never worked. So there are no minuses for not doing it, but you get some small plusses for doing it.
If you use GWX they are all disabled anyway, as the question arises why would you be rewarded for simply doing your job?