Why would a VOR be decommissioned leaving the DME? As can be seen on this question and this question the OJC VOR has been decommissioned but the DME is still active. What would be the purpose in having DME without VOR?
Many older Air Transport Airplanes have no GPS. I'm a pilot since 1970. I operated A330 for 5 years until 2000 without GPS. The average IRS position (Inertial Reference Systems) in the FMS was updated by DME/DME. On older airplanes we selected the DME Stations manually preferably with a 90 degree cut-angle to obtain an accurate update. A single VOR/DME station could be used for update as well but it's a lot less accurate. Example, if you are 60 NM away from a VOR, a 1° error in azimuth would cause an error of about 1 NM. All Airbus aircraft have an approval for RNAV Approaches down to an accuracy of 0,3 NM with 2 DME stations available. This is why DME's are still useful, many ILS have a DME. Conventional VORs are terribly inaccurate, Doppler VORs are much better even down to a lower altitude, but requires more space.