The story I heard was that when DMEs were first introduced to replace the markers, they were going to be colocated with the GP, but the GP equipment huts were not big enough to accommodate the TXs - so it was decided to locate the DMEs with the LLZ rather than build bigger huts/sheds.
The DME can be zero'd to the runway threshold, if necessary.
Places like Korea & Thailand use this de facto US standard. The DMEs are not THR zero'd since this causes maintenanace issues. I have heard that the proposed third runway at Inchon will have the ILS colocated with the GP - but the existing ILSs will be LLZ located still .... be careful out there