Yes, it is the way Airstream set the units up. Yes, it is a long term drain, about 6 mA but even that over months of storage will kill the batteries.
I put a switch on mine. I got along neck (for thick panel) toggle switch at ACE hardware for about $10 and wired it in to the LP gas detector. I put another one on the Sony Radio, which will come on "disco mode" if you turn the store/use switch off and then on again. Since the radio is behind a closed door (in my trailer anyway) you can't even see it is on. And it takes a lot of power, almost an amp, with it's lights flashing but doing nothing else. A real battery killer for sure.