At the time my Morgan had a nut and bolt rebuild, Kevin (the restorer) created a strong and very smart fibreglass locking travel case, the external finish to match the cars colour and internal trim of the case also to match the the car`s trim, with a well sized Morgan script in silver, all very smart indeed. For additional security the case could be fixed to the rack using stainless steel "P" clips, which provided a degree of comfort if we stopped for lunch while passing through towns or villages. We have also used the case on weekends away, , we toured France, Spain and Italy making good use of the case, which all in all worked out rather well.
As others have suggested weight can be an issue IF and when you dismount it to carry it up flights of stairs and trying to protect it`s perfect painted surface in some old Château or other overnight accommodation while touring was difficult enough in my fifties, now twenty years on... The best plan is to make use of soft bags that can be lifted out of the case, leaving the case mounted on the Mog.
https://www.tm-img.com/image/gPiXH