FYI: Modern inverters typically have two stages, first a voltage stepup stage, then a DC-to-AC stage.
Stage 1: 12V battery voltage is PWM modulated and stepped up to 120V AC, then rectified to 120V DC.
Stage 2: 120V DC is modulated to Modified Sine Wave 120V AC.
Now for most typical RV usage, the 120V DC from stage 1 would actually be better to run appliances off. This saves the DC to AC conversion loss in the inverter and the AC to DC conversion loss in most power supplies. Only old style transformer based wall wart (the heavy type) need the AC. Induction motors run off AC, but they are unusual in small appliances because they are heavy. Aside from my furnace blower, the only induction motor I have is in a heavy duty pressure washer. Older washing machines have AC motors. Newer washing machines have brushed universal motors or (better) brushless motors.
Likewise most other household appliances work well on DC.
Examples: heating appliances: AC or DC doesn't matter.
universal motors: these run off ac or dc likewise. It is the typical motor found in mixers, hairdryers, power tools etc.