I found the hitchlock was prone to be wet with condensation when using a hitch cover so I abandoned it. The design of my hitchlock offers some protection from rain anyway. Also the cover rapidly became faded and tatty looking and I rather resented advertising the caravan dealers name - having had some poor after sales interest. Condensation build up is also why I do not use covers on the two electric sockets on the car but just rely on the spring loaded flap.
I suspect there will be many who hold exactly the opposite view though so I imagine it is a matter of trying both on and off and seeing what suits your particular set up.
IF you leave the cover off the red plastic fittings will eventually degrade and harden. The handle on my AKS 2004 is a bit dull and white. On the previous 'van the handbrake handle disintegrated.
We use a hitch cover at home when the caravan is not in use to stop components constantly going through a wet - dry cycle (more wet than dry these days!), avoid UV and general degradation of plastics and to avoid debris getting into various parts of the system. But away, it's just another annoyance I do without.
Cathryn's point about security is quite valid though. A matter of choice.