if DME was required on an ILS (and that would be, of course, prior
to the final approach fix), that it would be shown as a "DME required"
note, rather than as part of the name of the procedure.

That's the way it's becoming, but, according to Wally, that's only in
order to conform to ICAO standards.

There ARE some ILS DME approaches out there (or were). Can you
explain how DME would ever be needed to fly final approach on an ILS?