I track both - My computer calculates using moving time and my android app calculates using elapsed time. For the current month my average mph on my 20.5 mile commute is 15.89 moving and 14.04 elapsed. I seem to go slower in the morning and have my best rides coming home. I had a PB of 17 mph moving last Tuesday afternoon - it felt great.
I respect anybody who can hold up a 19 mph moving speed for any significant distance.
Commuting is about 95% of my riding, so why not monitor my progress, and ride it hard? Improving my average speed on my commute is my second-favorite thing to work toward, after the weight that I have been losing since I started exercising regularly.
I'm a big guy on a heavy bike with loaded panniers but it doesn't stop me from loving to go as fast as I can.