I've rarely seem them covered and never did so when we had fivers.
I used to remove mine when I needed the space in the bed or if I did not plan to tow for several weeks, but its simply a matter of preference. Whether in or out of the truck, grease the hitch mechanism at least once a year.
The only time mine has been removed was to put the bed liner in. It's supposedly "easy" but it's also heavy.
I covered it once when I had to use it to haul trash when working away from home - at home we use a utility trailer an another vehicle for light duty hauling. I used a canvas drop cloth and bungie cord (we were painting a house).