Do you think ATC would cope with pilots being unable to accept any instrument approach?
I think that's quite different to having traffic which can in all cases fly the ILS down to 200ft (or whatever), and with nearly all CAT being able to fly it even lower.
Your point about a wide range of operator minima [not being ATC's business] is on the mark but at the same time this is what makes the case for any sub-full-IR privilege very hard to make, because "the other side" is going to argue exactly this line.