...Or perhaps the fourth crystal was already cracked, which is why it wasn't in use at all, but was put
to use when there we no intact crystals left?
"Mudd's Women" does seem to establish that battery power was needed to supplement other remaining sources of power after three crystals were lost, and still gave reduced performance. So the loss of the three crystals
a) didn't result in the loss of all power other than battery power (because it's "supplement" rather than "supplant")
b) reduced performance
which may mean that loss of a crystal results in a drop in power and loss of three results in three cumulative drops but only a loss of a fourth would drop power to zero. But it may also mean that a single crystal is working at any given time, giving full power, and the battery power had to be added because the fourth crystal to take on the job was inferior to the first three (that is, it had a crack in it).
Later we hear Spock say that all the ship's power is running through a single crystal. Supposedly, then, this is unusual. But Kirk is not worried: his suggested remedy is using bypass circuits, which Spock then says were burned during the chase. Remember that when the three crystal circuits blew, Kirk was on the bridge, and we never heard anybody in the transporter room tell him about the crystal circuits blowing. Spock only heard of all of them being gone because he was present at the transporter room. Sulu on the bridge commented on "another" being lost, meaning the bridge team necessarily knew of at least two losses, but possibly only
knew of two losses rather than of the alarming situation where there only was one crystal left.
Again possibly a reason to think that loss of a crystal has no observable effect if a spare can be brought on line, and Kirk never noticed anything seriously amiss because spares did come on line, one by one?
EDIT: oops, you beat me to it, Bob! But see the different nuances in the rationalizations, with a "pre-cracked inferior spare online with batteries" vs. "battery power until inferior pre-cracked spare can be brought online".