Greasy balls are a very common issue. I've even heard of folks placing a piece of wax paper over the ball before setting the hitch down. I see two extremes, the bone dry ball with the usual rough spots wearing deeper into the dry socket as it turns like a mill. The other extreme is the greasy ball that is covered in gritty grease since all the dirt sticks to it making a fine abrasive compound to wear the socket sooner. This dirty greasy ball is a mess all the time and always gets on your leg.
The best solution is to apply grease to your clean ball and socket before hitching and then clean the ball off when you unhitch. Don't forget though that the hitch is greased too and could collect dirt so the overly cautious operator would clean both ball and socket after each tow.
I only clean the ball and regrease with fresh bearing grease. When running a dry ball I find that grit is generated from metal wearing off of either ball or socket. Also, the bullydog style hitch works by clamping onto the ball and I believe it needs to have lube to slip.