I agree. It makes no sense to me to have two divided like this.
Running a residential fridge off an inverter off one battery? Yikes! For that reason alone I would connect the two batteries. They do not have to be exactly side by side to connect them, but use a very heavy gauge wire to connect them. Many trucks will have their two batteries on either side of the engine bay.
How are the batteries connected? Is there a solenoid that connects both to each other when plugged in and disconnects them when not?
Or the charger has two outputs?
Or a large diode?