Use the battery to power AC startup surge in an RV
Many RVs come with generators, and the air conditioner is the item that demands it be a high power generator. The Generator needs to be big enough to run the AC, and in theory let you do other things like microwave when you run it. It also has to be big enough to handle the surge that the AC motor takes when the AC starts up.
This surge is huge, and will often overload a generator, particularly external generators that are commonly used on smaller RVs. To fix this problem, there's been a bit of effort to develop "soft start" electric motor technologies that start up motors slowly, and store charge in a big capacitor in order to provide the surge.
However, the RV also has a deep cycle battery and (if a motorhome) an engine starting battery. Both these batteries can usually deliver 100 or more amps in a burst. (The engine starting battery can deliver several hundred.)
Today, high-power inverters have gotten much cheaper, even those that can deliver 500 to 1,000 watts (and peak to far more) are getting cheap. I have wondered why it has not become standard to include a high power inverter in any RV so that small 110v appliances can't be run off the battery for short times, rather than firing up the generator. To microwave something for 30 seconds requires starting the generator which is quite wasteful, and also noisy. Of course, what runs off the battery should still run on 12 volts, and some things (like the fridge in electric mode) should not run off an inverter. Short microwave bursts, and a few hours of flatscreen TV watching can run off an inverter.
And so my proposal is that such an inverter also be available to provide surge power to the AC compressor when it starts, even if the generator or shore power is on. The extra 1000 or so watts the inverter can provide would allow the use of a smaller, cheaper generator. This requires an inverter that can sync to the phase of the incoming AC, and of course safety circuits to assure that power is not fed back into the shore power port when it is disconnected.
Today, the big trend in generators is actually to have them use such high-power inverters. The generators are thus free to generate dirty power, and to run at whatever RPM is best for them at the time. The inverter cleans up the power and puts out clean, constant voltage. There are modest losses but overall it's a win, as you get a generator that is much more efficient and quiet, and better quality power. Many suspect that RV generators will switch to that approach. In this case, it becomes much easier to have an integrated inverter generator able to also draw from the battery for its surges. No need for grid tie logic in this case.
To wit, one could see a system where a 2kw inverter generator, able to boost to 3.5kw by adding in the battery, could be enough for a typical RV, even with a decent sized AC. You might have to have a circuit that says "If the microwave or other big load is on, don't start the compressor" but that would only be an issue if you wanted to microwave something for a long time on high. Note in a proper AC the compressor is not running all the time, so the AC would not be off -- it would just not be doing on cycles during the microwave use.
There would probably be some 110v plugs in the RV which are marked "On under shore or generator power only" vs "always on," or possibly switches to control if they are on the inverter or not, since there are loads you would want to make sure stay off if running only on battery. A little more complexity to the internal wiring, but a big saving on generator size and a better dry camping experience. It also means a more usable RV when plugging into a 15 amp external shore power line. In many RVs, plugging into 15 amps is not enough to start the AC, and certainly not enough to run the AC and another device. The power control system would want to know if it's plugged into 15A, 20A or the normal 30A. And it would also want to notice if something is drawing too much battery power and shut it off before the battery gets too low.
Obviously as well, the 12 volt converter and battery charger must only run off true shore power or the generator, never off the inverter!