Our copy chief has pushed to get the desk respect in the office. It hasn't always worked, and more often backfired. We are the brunt of reader complaints and the chief takes a lot of criticism and complaint from the editor in chief, even if the problem is not that of the copy desk, but the city desk, some other department or plain lack of news. We have a pretty good relationship with the city desk and its reporters. They are all pretty receptive to constructive criticism and input.
Business is occasionally open to suggestions but often takes corrections personally.
We don't have much to do with sports. Four of our copy editors do the majority of the layout for each day's paper. There are no rewards. It is an expected part of our duties. I'm not sure.