This is aimed at Single-engine warbirds. P51 rides are going to be really boring when you can't touch the stick.
I would say that the vast majority of licensed pilots probably SHOULDN'T be touching the stick (unlicensed passengers are right-out). Every aircraft has its quirks, but these aren't ultralights and Cessnas we're talking about. I'm not a pilot myself, but the way I see it is similar to the difference between being able to drive a car and riding a motorcycle. Just because I know how to drive a car, doesn't mean I'm qualified to take a Harley out for a spin (or perhaps more appropriately, a street-legal daily driver vs. a high-performance NASCAR machine).
One definitive solution would be to drop the exceptions for warbirds in the existing regulations outright, and develop new licensing and regulations specifically FOR them (which if I'm reading that document right, is precisely what they'll be doing).
I did not read that two page file, but what if you want to take a lesson in it? You can't do that without touching the stick.
As I said, if they're working on rolling out licensing and regulations specifically covering warbirds I'm sure this will be covered.
It's clear from the document the FAA DOES recognize the importance of maintaining these historical machines and keeping them flying, they're just trying to determine the best way to cover the legalities of doing so.