I'm a bit of a hippie in that I'm biased towards innate creativity and improvisation as opposed to strict learning of traditional established forms of music.
I realize that's a false dichotomy but it's semi-useful.
I only took a small number of music lessons but they were definitely focused on learning the exact way to play finished songs by established artists. There's nothing wrong with that, it's quite satisfying to play things you recognize, and it's probably easier to teach in some ways.
But improvisation is such a magical, living thing. I haven't tried to teach someone in this way, but if I did, I would focus on exercises exactly like the one you describe.
I would show the student how beautiful music can be created spontaneously through the application of patterns and "restricted subsets" (scales, chords, etc).
I've met some people who work with musical therapy. I believe they focus on this type of thing a lot. I don't know why in years of music class in school I never came across anything like it: free improvisation based on restricted creativity.
Once I noticed that the black piano keys are a pentatonic scale... Just sit with your eyes closed, spread your hands out and feel the black keys. They're raised and so easy to find. try not to play adjacent black keys. Do this with both hands. If you want higher or lower notes, move hands in that direction. Play with rhythms. Play a pattern on one hand and just let the other bounce around. find a few interesting chords to come back to - resolve to. But most of all, do this with your eyes closed. You'll be surprised what comes out after a bit.