I always presumed the stations were cutting power to save money, but then why
would it be based on light vs dark, rather than on time of day?


Power and/or pattern change is done to accommodate a station of lesser class
against a station of superior class; or a station of the same class, but one
which was authorized before the subject station.

AM is a "demand allocation" scheme, and the first station to be authorized is
usually the superior station, with respect to subsequently authorized stations.

Extreme example: 710 in L.A. and 1510 in Boston are protected by stations of
higher class (710 in Seattle and 1510 in Nashville) simply because these
stations were authorized before Seattle and Nashville were authorized. L.A. and
Boston remain Class B; Seattle and Nashville became Class A.

Power and/or pattern change is not always at local sunset or sunrise at the
affected station. It could be local sunset and/or sunrise at another station
(see 1110, 1530 and 1560 for examples). There are historical reasons for this.

So-called DA-3 operation is also possible, where a station has defined day and
night operating parameters, but during so-called critical hours it operates
differently, usually with parameters in between day and night, although not
always.