hmmmm, your not the only one that was thinking about that, I needed to retire a fleet truck and had the choice of a 12' box or my Chevy 2500 diesel with a service body. I planned on a mini adventure conversion for the kids and I so was weighing the power/mileage of the Chevy, against the room of the box. The 4' width limitation of the service body lost out. Although I will say the service body never gets ticketed, even when working over night, and with our rules on oversize vehicles here the box always will.
So for stealth though I think you are right on, a service body never stands out anywhere commercial or residential, as it just looks like a service call which happen 24/7.