Do you have a diesel that should not be idled? With gas engine you do not have to drive the vehicle. Just run the engine.
Doubt that the charge time will be much different. As the house battery gets charged the rate of charge will be reduced well below the limitation caused by the 30% inefficiency.
My 1000 watt Magnum MMS1012 has a max charger rate of 50 amps so that is my limiting factor with the two inverter system. Not the capability of the alternator or the vehicle inverter.
It is very important to me to charge the battery correctly with a 3 stage charger with temperature compensation. Shorter battery life is expensive.
I was pointing out that efficiency is not just measured by fuel costs. For my application, other inefficiencies of the extra inverter scheme come into play.
But to address your points:
Idling the engine is not a desirable option for me.
There is no high idle option with gas engines, and the alternator output is much lower at idle than when driving, so charge time is extended.
Since I would not leave a vehicle running if I'm not there, I would need to be sitting in the (exhaust laden) campsite, instead of going off hiking, fishing, etc.
As the charge rate drops (with whatever engine driven charging scheme), and the system drops out of bulk mode, my solar can (mostly) handle the absorption and float modes...along with most of the day-to-day loads (LEDs, H20 pump, MaxxAir, etc.). Except on the very darkest days, it now does that. What will cause my system to need a boost is the use of stuff like the microwave, lots of house heater fan on a cold night, and possibly the fridge (TBD).
So, bulk mode mainly sets the time I must drive. Unless the batteries are completely flat, bulk mode charging rate...even without temperature compensation, is likely to be well under what the batteries can accept safely.
With the VSR, my charge rate isn't limited by either side of the extra inverter design. My MS2012 isn't in the circuit at this point. The only time it will be used as a charger is when I'm on shore power (rare if ever when not in storage).
Yes, decent and large AGM batteries are expensive. But amortized over the lifetime of the batteries, the cost of a (possibly) somewhat shortened battery life is acceptable to me. I don't think I've ever had a car, motor-home, or trailer camper battery die in under 5 years. All charged by alternator alone. Many without any modern 3 stage charger available, even for storage. So for my use, possibly extended battery life doesn't outweigh the trade-offs I'd make with the extra inverter design.