Engine starting battery being charged while parked?

All of your remark and question is an open discussion.
Some coaches don't do a good job of caring for the house bank when on shore power. That can be fixed with a good converter/charger. Once you know you have a good converter/charger, then there are numerous devices that can connect the house bank to the main engine start battery and keep it properly maintained. They are not expensive, but I have not yet seen a production coach equipped with one as standard equipment from the factory.

Matt