I ran my 71 Moss Box Plus 8 with a belt for nearly 10 years with no ill effect. See pic. This pic was taken right before I sold it, and there is no damage from the belt.
I did have the sheepskin version though and I have that same style on my replacement car, the 86 Plus 8. So I cannot collaborate the damage experience.
In my experience, it is the belt in many cases that identify the car as a Morgan or starts a conversation with admirers.
Cheers.
Mark
1934 SS MX4 1938 Series 1 DHC 1951 Plus 4 2005 Roadster