I use an adjustable voltage power supply exclusively for plug in charging duties. Mine has a shunted ammeter/voltmeter amp hour and watt hour counter on the DC output, and some additional computer fans added to the casing.
These fans and ammeter, would still run when there is No AC available, unless I disconnected the Anderson powerpoles.
Now, I use a 50 amp 'Ideal Diode' so when I unplug from AC, I do not have to unplug the DC connector from the power supply. The ammeter and fans shut off instantly when I unplug from AC.
The Ideal diode only loses 0.04 volts across it at 40 amps, as opposed to the 0.4v+ of a silicone diode, but even if there was a non negligible loss, I could just turn the voltage dial a little higher to compensate. I also parallel other power supplies/ chargers when 40 amps does not float my boat, and the Ideal Diode perhaps keeps the power supply happier.
It's my opinion a adjustable voltage power supply yield vastly superior charging to automated 3/4 or 12 stage chargers( the 12th stage is fellating the proud smart charger/ battery owner), and they do not get confused when there is loads on the battery while charging.