Inverters are becoming more common from the builders especially with more and more coach models coming off production with a residential fridge. My coach did not come with one but I installed it myself. Not difficult but my back ground is electrical in nature so it was pretty simple for me. Dealer install cost will depend on the complexity of what you want. Complexity = more labor time and material cost. My invertor is a small 800 watt unit. Primary use for us is to run a slow cooker, TV, DVD, computer, table lamps and such when we do camp without shore power. No microwave oven, morning coffee and such for me. I need my generator for those items. With two medium size batteries I can last a day or two with good power conservation practices before I need to recharge the batteries.
Invertors and installed battery capacity will determine what you can and can not operate and for how long. The coach air conditioner normally should not be operated off the invertor. The amount of power the unit demands can tax the limits of an invertor and can deplete the batteries very quickly. Coffee pots or other such heating devices (hair dryers, space heaters, microwave, toaster ovens) are not far behind. I'm not saying you can't run such appliances but there are limits that will depend on your configuration.
For us we can use the TV, DVD, satellite receiver, table lamps, clock radio, laptop and such. Adds a bit of flexibility for us when shore power is not available and I do not want to run the generator. Also I do not have solar panels.
2006 Hurricane 31D built on a 2006 Ford F53