With a modern battery charger left on, powered by the inverter or shore power, once the BT battery is fully charged and the charger goes to float, the power drain will be minimal. So I don’t see it as an issue when out cruising, nor when on shore power. If you were going to leave the boat on the towpath for an extended period, one would switch the inverter off and then no power drain. Unless that happened a lot and you switched the power off very shortly after mooring (which is unlikely because most people wander around doing stuff for a while before leaving the boat for an extended period of time on the towpath) I can’t see it as a problem, and no worse a problem than charging at 12v DC over long fat cables via a VSR.
We don’t have a BT but if we did, I would want it charged by a local mains charger.