Yes, but going from a 12v battery to 120v from the inverter has some power losses. Going from 120v from the inverter back to 12v for the device has some power losses. In total, when using an inverter to charge what you can plug straight in to a 12v outlet costs you about an extra 10% to 20% of the power. When we are boondocking, I don't want to throw away that much power.
On edit: I went to the WFCO website (the Airstream's inverter is a WFCO) and even WFCO claims ">80% efficiency." If something can be powered directly from the 12v battery, it is MUCH more efficient to do so.