Indeed, one of the interesting things about a world with "forgery museums" is how much less protected they would need to be.
Imagine if the public were actually allowed to touch the (replica) painting. Sounds crazy, doesn't it? If a reproduction was a $30K capital cost for scanning and oil synthesis, followed by a $2K marginal cost for reproduction, though, why not let the public touch it? Just print another one each year. Heck, destroy the reproductions when you would normally rotate them out of display, and then print them again when you want to install them anew.
For that matter, imagine if one could study (excellent forgeries of) old masters in their local museum/gallery, instead of having to fly to Europe. In fact, imagine if you could "run off" a replica for group study in art school from the room beside the offset printer!