Interesting, Dave. Running it on 110 is a good fit for your scenario when plugged in at home and only minimally charging.
I checked with my bud and he did say that with a whole-house inverter that situation mentioned above could happen (I hadn't realized that). He manually puts his refrigerator to propane or AC power, so that when the inverter is on (but rig not plugged in) it will not go to AC (running from the inverter/batteries, which would not be good!).
I guess there could also be a way to wire the refrigerator (AC/DC one) so that when on shorepower it would run from 110, and when on inverter/battery it would run on DC, but my brain is feeling overstretched at the moment
I only have a charger (not inverter) so have not figured this out for my own rig.