I don’t have a SQM either, but I still find the numerical value useful, and for essentially the same reason as you like the NLM.
Both give an indication of when the brightness of a stellar object is comparable to the brightness of the sky when observed with a particular optical train and detector. My eyeball is 100 times (5 mags) less sensitive than my CCD and has a resolution 30 times poorer (circa 1arcmin compared with 2 arcsecond seeing limit), so one resolution element of my eye collects 900 times as many photons as in one of the CCD, another 7.4 magnitudes.
Plugging in the numbers, a NLM of 6.3 corresponds to 6.3+5+7.4 =18.7 sky limit for my scope.
The corresponding instrumental estimate is 21.2 – 2.5 * log (2 * 2* π) magnitudes for the sky, which evaluates to 18.5.
That is a remarkably satisfactory agreement!