Any time you have metal to metal contact with friction you are going to have wear. The idea of the grease is to reduce that friction and therefore the wear.
Almost every single hitch manufacturer, with the exception of one (Andersen) that I am aware of, recommends the use of some type of grease on the tow ball. There have been instances of people not using grease and hitch ball came loose in the head because of the friction and turning motion during turns.
In addition, if you have L shaped WD bars that insert up into the hitch head you should grease those bars every time you tow. There is a tremendous amount of pressure between those bar ends and the hitch head receptacles. Dry bars will often make a lot of squeaks and grinding noises. Over time, the bars ends will wear into an oval shape and the inside of the hitch head will wear quite badly on the bottom edge closest to the trailer. When this happens, you will get less and less WD from your bars and find you have to take up another link or adjust the bars up tighter. This is a clue that your bars are wearing out. Contrary to what was implied in a previous statement - a hitch head or WD hitch does not last forever.
I used to remove my bars at the end of a towing session and wipe them off along with the ball before stowing away. Then I would apply a light coating of wheel bearing grease before every new tow.
Did this routine for over 50 years until stopping towing recently. Always worked for me! :)
Barney