Gdetrailer,
I used to believe in stand alone inverters, and stand alone chargers. There is no question that is cheaper. However, I do love having "load support" on my inverter/charger.
When I had limited shore power (10 amps) I would often do "dual conversion" where only the converter was plugged into shore power. I ran the RV from a 2500 watt Cobra inverter, rated to run motors.
If I were in a "do over" situation I would get a Victron inverter/charger, with their version of "load support" (which is NOT voltage support).
The ability to limit shore power demand is important when one does not have access to the shore power breaker box, especially at -25 C (-13 f).