Una Corde should NEVER be used as a VOLUME change, but as a TIMBRE change.
Hence "una corde" during Forte passages, etc.
Yes, you do see "una corde" often in tamdem with Pianissimo passages because the composer wanted both a softer tone and timbre change.
The #1 mistake in using the pedals is using the u.c. as a crutch to play softer.
Also, keep in mind WHO the composer is... Debussy, for example, used "con sordino" to mean u.c., where as we would typically think of "con sord" as "don't use the damper pedal."