Usually a procedure is developed as an ILS/DME if no other means are available to reference important parts, points and segments of that approach.
For instance, let's say there is no VOR with which you can verify your location over the outer marker. Or let's say there is no way of verifying your missed approach point when the GS becomes suddenly inoperative and you revert to a LOC non precision approach? (Remember you can climb but are requested to not turn anywhere until you get to that golden MAP).
Also in modern installations the DME has become a cost effective solutions to replacing the marker beacons in their entirity. You can verify the equipment from one centralized location and don't have to worry about 2 sometimes 3 more installations (ref: OM, MM, IM).
As for your original second and subsequent questions. If a procedure is named an ILS/DME approach, you can consdier that a contract between you and the local aviation authorities. Therefore if the DME portion is notamed out of service, the procedure cannot be used.
Usually most of these procedures will note RADAR or DME required, and then as long as you are within positive RADAR control, you are allowed to use that approach even if the DME is notamed.
As a final note. Please search on youtube for an Air Newzeland 757 (maybe it was a 767) that had made an approach to an unmonitored ILS and have gotten errornous glide slope indications. Referencing a DME or any other kind of locator, intersection verification vs. altitude provided their life saving ticket.
Air NZ and errornous ILS indications.
Good luck!