Paul

Attention for the “undercurrents”, the melodic quality of accompanying lines.

So not forcing the student to play what’s written “because that’s what one should do”,  but tempt and challenge: just try it, try it seriously, with attention. With an open mind and ears.
To train the skill of listening, focused listening, detailed listening. While you play. Which is not that easy at all.

Taking all this into account on could say the una-corda pedal can be used as a kind of equalizer, changing the timbre of the tone. Like a sound engineer when doing the master mix after the music has been recorded. The pianist does it in real time, while playing.