The FMC birds use DME too to check and calibrate their data. Watch the autotuned stations there. They are not only used for rough estimates.
It's a difference if you can monitor external nav sources and relative positions to them or if you have an internal nav source which tells you where you are, just by calculating and watching some gyros.
Well, those sources and systems are coupled today, so a GPS works together with an IRS, getting checked with DME to achieve a high level of accuracy and also failsafe operation.
VOR broken or in maintenance? The INS will still be fine with any other DME it can receive while showing your position on a digital display instead of using a fluctuating needle on an analogue gauge.

With a VOR you can fly radial 212 until 12nm out and then turn left 30 degrees. With an INS (calibrated through any DME in 200nm range), you can fly spot on any given coordinate you enter.
It also shows you the current wind, your offset, your GS and can calculate times, speeds and headings between waypoints.
Enter any fictional waypoint of a fancy RNAV procedure and it will show and guide you to it while the VOR guy has to set up his radials to get to N 44 47.2 W 063 18.1 and may miss it when speaking about accuracy.

The INS also guides you when there's no VOR in range. It runs down on accuracy slowly, but you always have your very own nav source on board. With three units, they also crosscheck and enhance each other.

Man, I could sell those things.  ;D
But agree, you have to like these old 7 digit boxes when you operate them in the sim, where all VORs are working, where needles rarely fluctuate and where nobody gets harmed if you miss a spot.
But after a while, they will show more use than just entertaining you with their need to get an update, that's for sure.  :D