I've always made the cultivation of creativity a primary focus in my teaching method. One of the main ways of cultivating your creative side is by increasing your improvisational fluency. Improvisation unlocks the potential for not only being a reproducer of notes on a page but also a creator of music. When you give the music you play some of your own self-agency by creating it in a spontaenous moment, the music becomes a part of you. The relationship between you and the music changes from something external to internal. This shift more often than not, in my experience, deepens a students appreciation for music.
Here is a great clip on the neuroscience behind this phenomenon. The brain tends to get "bored" with rote learning via notes off a page. Improvisation seems to engage and help a person regain an interest in musical activity.