The only exception where I'd look at an inverter/charger is the Victron or Magnum Energy "hybrids" that are always inverting, and power is passed to the batteries first. The advantage of this setup is that if the CG has low voltage, the inverter will start using the battery to maintain the proper electricity for components, which helps with A/C compressors that can burn out if started or run at under 100-110 volts for periods of time.
Just to clarify these inverters mentioned are not always inverting and they do not maintain proper
voltage at the loads. These models still have a transfer switch and when the inverter is
ON it is in
parallel with the loads so it will add
current by inverting from the batteries but it does not have the ability to raise the voltage. It is possible on a small generator to see the voltage increase but that is only because the inverter is adding current which in turn lessens the load on the generator allowing it to raise its own voltage output.
I hope that makes sense I just would hate to see someone spend more money on a hybrid model for the wrong reason.
Gary