Although arg, I'm under the impression that the battery monitoring is 24/7, so it never "powers down". Maybe not?
Well, this is all Tesla's secret sauce and we're speculating as to the details - likely there is some monitoring that's 24/7 (or at least, polling at regular intervals throughout 24/7), but it will want to be more intensive when actually drawing a load. And the coolant circulation doesn't generally run during 'sleep' while it does (to equalize cell temperatures) during charge/discharge. Maybe you could argue that you could draw just a little bit of current through the DC/DC without doing coolant circulation, but then you need some way of monitoring that - maybe the DC/DC converter can tell you from its duty cycle, but then you've got a chunky DC/DC with intelligence in it, which has probably stuffed its efficiency at very low load......
It would be fascinating to know the full set of trade-offs that led to this design, but I doubt they'll ever tell.