I like the idea- it sounds more interesting than using a straight crew calculation, but maybe some hybrid might work more "realistically"?
In terms of CR deployment loss, would it be feasible to base it on the proportion of fleet points of both fleets?
For example, if a 30-point fleet squares off against a 10-point fleet, the 10 point fleet would take 3 times more CR than the 30-point fleet, which would sort of reflect the psychological state of the smaller fleet ("Why am I committing suicide?"). Perhaps it could be partially mitigated by crew experience- green crew are cowed by everything and take full CR reduction, but elite crew are hardened and take only some portion of the CR loss.
Well, my question is, why? You've provided a lore explanation for the change, but one can provide a lore explanation for virtually every change, and that's not the same as providing a reason to make a change

(Btw, CR reflects more than just the crew's mental condition, in fact it's leaning more on the side of "overall condition of ship".)
"More realistic" by itself is not a very good reason, either, not without careful consideration for the impact a change has on gameplay.
For CR loss after combat, maybe it could be based on amount/severity of damage taken? A fleet that is nearly annihilated would be nowhere near combat ready, and ships that suffered engine shutdowns and multiple disabled systems would similarly be less ready.
That's actually there - there's a CR loss for weapons/engines being disabled in combat. Might end up replacing that with a straight calculation based on hull damage taken, though, to simplify things.
For recovering CR, in addition to using supplies, maybe there could be travel modes where a fleet travels at some percent of it's full acceleration/speed to increase its rate of CR gain. Faster fleets might be able to regain CR faster than pursuing fleets, which could reflect a "harrying" situation? This all might be needlessly complex, however.
Hmm. I've got some ideas kicking about re: "alert levels" which, if implemented, would be along these general lines.