Sorry, but this is wrong on many levels. An inverter isn't any harder, and most likely easier than going without because anything that would normally plug into the wall will.. Well... Just plug in and work.
Now the issue is you don't want to use just any old inverter as there are major differences between them. Get one with voltage stabilizing (does a good job of keeping a steady output voltage, just like the some home theater power centers do), and also make sure it's a pure sine wave. Pure sine waves run a bit more, but are much safer for sensitive electronics vs a non-pure wave system. The last one we did at the stop was a 2000watt RMS/4000 max pure sine wave that ran about $800-1000 (can't remember exact figure), but you can fine similar setups with less watts for a lot less money.
Also, use a good deep cycle or dual-purpose marine battery all the way around. Try to use the same battery in all locations, as using different batteries (different in style as in deep cycle vs a starting battery, or a smaller capacity vs larger capacities) can cause issues as one battery may fully charge before the other, but because of the load imbalance one may over charger or one may remain undercharged.
Also look into the after market audio areas for an alternator/generator. The same RV van I put the power inverter into above we also put a tsunami alternator which produced around 240amps at a fairly low rpm. We also used one of their heavy duty relays (500amp rated) to isolate the rear batteries from the one under the hood when the key was off so the main battery wouldn't drain and leave you stranded.
The setup used all home equipment (made a custom flip down mount for the 36" tv we put in), including the directv receiver and home theater system.