There isn't much reason to disconnect your batteries. In my opinion, as others have stated, the battery life you think you gain in the long term will be negated with one accidental full discharge.
In terms of the power supply/ vs charging arguments: The progressive dynamics units are really both. Since they are nicely filtered DC output that is always at a higher voltage than the batteries, the converter is indeed a power supply. Yes, it will run the 12volt side fine without batteries but just don't do it for the reasons already discussed.
In the past, poor linear ferroresonant converters had a laughably low charging current, like 2-4 amps... And they only acted as a charger because eventually the output voltage of the charger would rise up high enough to actually charge the batteries if there were not too many other dc loads powered on in the rig.
Executive summary: leave batteries hooked up when on shore power, check fluid levels once a month. Disconnect batteries if storing rig more than a day or two without power, to avoid parasitic drain.
