Perhaps the biggest advantage of an inverter is you do not have to reinvent the wheel. That is, most day to day items we want run on 120 AC. You do not have to wait for a 12 volt version to be invented and you have a greater 120 v selection.
Add to that the cost of rewiring a TT to handle the higher 12 volt dc current and the fact that the majority on the RVers camp with electricity; there in not much incentive to change.
For those who ask "why not forget all that stuff and just use a tent" the answer is simply "convenience". Either you get it or you do not. Likewise,those who question why tent? Tenting adds had a completely different feel to camping. Again, either you get it or you do not.
Finally why have a battery at all? Most folks camp with electricity. The reason is most TT owners expect a degree of self-sufficiency when camping. Historically that meant water, light and fire (cooking) these were gas or 12 volt. Today it include hot water, radio/Cd and in some cases television. Tomorrow it might include microwaves and coffee makers.
Fortunately if you do boondock, there are a lot of gas or 12 volt options.
Be safe