The CAA is not going to "see the light " as you put it about replacing DME with GPS distance as long as there are multiple identical ident for radio aids closely placed in Europe.
There's one local VOR (forget which) where every time I enter its identifier, my 530W gives me a choice between the one I mean, about 50 miles away, and one in France. I don't really see the problem here. Of course if you select the wrong one, you may fly into a mountain, or run out of fuel mid-Atlantic. But then that's true if you just enter the wrong identifier too.