I hear what you're saying, Vij. With Mehldau's music, I feel that the structured nature of his compositions is what makes the music not just intellectually stimulating, but emotionally stimulating through the mind. I think I've mentioned this before, but my dad says he likes Bartok, but doesn't like listening to him all the time because it's not naturally enjoyable to him, per se. For me, though, Bartok just stirs me like few other composers' music. The Prokofiev piano concerto I'm listening to right now might well be classified as "mind music" by some, but to me it's just so enjoyable. I don't pretend to enjoy it to be snooty, but because it just feels so good to me.
With what I'd call "straight" jazz like Monk, Coltrane, Miles, et al., the music is emotional, but it doesn't really involve the mind as much. To me it feels more like relaxing music. I think that Monk gets away from this a bit although the saxophonist on the album I have (Charlie Rouse) is a far more conventional jazz musician than Monk, and thus detracts from Monk's unusual improvisations. Perhaps that's why Brad Mehldau either plays solo or with only a rhythm section (bass and drums). His work really has the feel of classical music (for most of Places, anyway) because it just sounds so... "clean" compared to more standard jazz. His music has that intellectual sheen, as I've mentioned before, which strikes at the heart both directly and through the mind.