Aye, I can tell you from experience that logic "freezing" butt-humps any complex logic system.
Short reason? the "pulse" of logic quits moving entirely.
Long reason? Basically the same, its just that the game can, possibly, recover from it. Not likely though.
Logic allready has some wonkyness in it. (if the controlling logic is not in the same "entity chunk" as at least part of what it controls, the logic eventually goes dead.)
Why add more wonky?
And yes, I do agree that the visible state of an object should be different when there is no available power.
This means, mostly, Lights, as most of the complicated logic DOES stop working as soon as a ship goes into overheat.
(heck, logic stops working if it even takes 1 point of damage)