The only benefit you get from backfeeding the converter output into your existing 120V network is the convenience of local outlets all over the rig. The risks of the practice far outweigh this.
You have to remember to shut down every item in the rig that eats too much power to run off the battery (if it didn't, it would have been DC already as a boondocking convenience). Miss one, kill your battery.
This includes anything you may have plugged into an outlet anywhere in the rig and forgot to unplug. Including the outdoor socket(s).
If you plug your backfeed into the "far" side of a GFI circuit, you lose electrocution protection.
You have to remember to shut off the converter loop and manually put your fridge on gas. Oops, don't forget the water heater.
You have to remember to disconnect the shunt cable before using shore power (
"or else a large occurrence," as Dave Barry warns).
In short, you vastly multiply the risk of doing something you didn't want to do, with consequences ranging from a dead battery to a smoking cat.
If I were going to do this, I'd mount a very limited strip of inverter-powered AC outlets in a single place in the rig, and use that. That way, I could police exactly what was attached and know where my power is going. Also my daughter wouldn't absent-mindedly try to use her hairdryer when she was out of sight of everybody else in the shower.
My benchmark is that using the (DC) furnace for one night off the battery pretty much depletes it. There's simply not a lot of power to be had there.