There seems to be a significant amount of controversy regarding whether, or not, the towball/coupling interface should be greased.
A considerable minority seem to think it shouldn't be but, I haven't yet seen a single, valid, argument that supports the theory.
The interface between the vehicle and the towed trailer is metal to metal. The nature of the beast is that it moves..... sideways by some margin and up and down to a lesser extent. A towball/coupling combination in good order has quite considerable friction between the two and it is inevitable that wear will occur.
It is ESSENTIAL that the inside of the cup on the coupling is kept clean and lightly lubricated to minimise wear and stress.
Knott/Avonride, one of Europe's leading coupling manufacturers list it in their trailer maintenance schedule, https://www.knottuk.com/.../KF082-Trailer-Svc-Maint...
The 'HAYNES' Trailer Manual (authored by my old friend Brian Bate IEng MSOE MIRTE) ISBN 1 84425 2124 Lists it as the first maintenance item
The Police Federation Towing ROADCRAFT 'the essential towing handbook' ISBN 0 11 552022 8 states " you should ensure there is a thin coat of grease on the towball to reduce friction and minimise wear".
In 30+ years of trailer maintenance and servicing, I have ALWAYS lightly lubricated towballs and coupling heads. I see NO REASON to change my stance!
The exception to this advice is if you use a friction head stabiliser directly on the towball or a towball mounted cycle carrier which clamps on. In these cases, it is necessary to degrease the ball using readily available, proprietory, degreasers and to re-lubricate as and when towing again.