Alpha:
In fact ICAO have mandated that ILS must have its own independent DME
It's not mandated by ICAO but States do have the option to provide DME in lieu of marker beacons provided that the DME triangulation displacement is less than 20 degrees from the LLZ centreline and the distance accuracy falls within +/- 0.2 nm.
The choice to use DME in lieu of marker beacons, in areas where terrain constraint is not an issue, is invariably simply one of cost; States only have to maintain only a single system (the DME) instead of 2 (OM and MM in Oz) or sometimes 3 (OM/MM/IM internationally).