Well I used to be one who never used grease on any of my trailer hitch balls, I would sometimes give em a squirt of oil, WD40, PB blaster, kroil or whatever I had handy, or run em dry if nothing was conveniently handy. Then one day I noticed my hitch ball was having the nut work loose when i pulled the trailer even though I had tightened it with a 3/4" drive large length breaker bar socket. Luckily the lockwasher had chinged the nut enough to keep it from totally having the nut fall off.
From that day on...I have greased the ball with grease and I have never had a hitch ball work loose again on me so I will continue the practice of using grease for this safety reason alone! I usually just use the cheapest $1 a tube stuff from Rural King that I use in my wore out antique farm equipment but any grease would be fine in my opinion. My trailers live outside so grease helps the trailer coupler from getting all rusty up inside as well.