It is a strange state of affairs. I can sort of understand the no VED, if you only venture out a few times a year, but the no MOT thing is baffling.
My father had to sell his ash and fabric bodied 1930 Riley Monaco for scrap when the MOT was introduced. The tester said it had excessive wear in the (mechanical) brake linkages. I later found out that the brake linkages were designed with "excessive play" to reduce friction. There was, as far as I know, no exemption back then.
Just googled it: in 1960, when the MOT was introduced, that Riley would only have been 30 years old, so wouldn't have been exempt, even if the exemption rule was in place, which it wasn't.