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

As with so many things, "It depends"!
It depends on how the coach is wired. It depends on what modifications a previous owner may have made.
I have heard that SOME brands of coaches are wired so the converter charges the chassis ("engine starting") battery. I have owned a Pace Arrow, a Tioga, a Southwind, all by Fleetwood, ranging in year from 1977 to 2002.
I also owned a 1988 Suncrest (an "orphan" brand).
NONE of them were wired so the chassis battery charged from the converter.
None were wired so the chassis battery powered the house electrical system.
I have rarely had a problem with the chassis battery being discharged from sitting for up to 13 weeks. Several months, yes, the parasitic loads are enough to drain the battery.