Disclaimer : 'tonality' is a word with a number of meanings - I'm focusing on the 'use of the diatonic scale' aspect of tonality here, as I believe that's what your question highlights, rather than 'having a tonal centre'.
I also find myself enjoying some wicked crazy jazz solos that are completely all over the place, hopping in and out of tonality like it's nothing.
Good! Because it is nothing. By which I mean, there is no important qualitative distinction between how the diatonic scale works, and how the chromatic scale works. (Well, perhaps there's one, which I'll mention later).
If we take the major scale as a prime example of our (tonal) diatonic scale, we have:
- a primary note (the root)
- a second group of notes that have a direct, strong harmonic relationship with the primary note. Arguably, these are
- the major third (5:4 ratio in just intonation, corresponds to the 5th harmonic of the root)
- the perfect fourth (4:3; root corresponds to third harmonic of the fourth)
- the perfect fifth (3:2, third harmonic of the root)
- arguably, major sixth (5:3 ratio)
- a third group of notes that do not have a strong relationship with the root, but do have strong relationships with the second group of notes. We could say that these are:
- the major second (has a strong relationship with the fourth and fifth, being their )
- the major seventh (has a strong relationship with the fifth, being its major third, and the major third, being its fifth)
Now, there are other relationships that you could mention, and that line between the second and third group is somewhat arbitrary. Nonetheless, at least in the case of the major seventh, it's pretty clear that its claim to be in the major scale is its relationship with other notes in the scale; it has a weak relationship with the root.
You could consider that the major seventh is, "in spirit", a 'chromatic' note lurking in the major scale itself, because of this 'once-removed' quality.
It's also a note that allows a number of interesting options:
- The establishment of the fifth as an alternative tonal centre
- use as a leading note that, partly because of its dissonance with the root, makes some listeners feel it should resolve up to the root
- complex harmonies like the major seventh chord. You might think this would sound dissonant because the root and major seventh are a semitone apart, but the strong relationship between the major seventh and the other two notes in the chord pulls it together, albeit with an interesting, complex quality.
Other notes in the chromatic scale are basically there by the same logic as the major seventh : they don't have a strong relationship with the root, they do have strong relationships with each other. So if you've already accepted the major seventh in your major scale, there's no logic by which you shouldn't use the other chromatic notes too.
Well, as I said earlier, there is perhaps one reason - the fact that on fixed pitch instruments, all these possibilities can only be opened up to their fullest extent with the use of equal temperament. But if your ear isn't offended by equal temperament, there's no problem.
So I'm (politely!) saying that I think that the premise of your question (that there's an important difference between diatonic and chromatic playing) is wrong.
My question boils down to this, what is chromatic playing good for in terms of emotions it can paint?
You can't directly paint emotions with notes; what emotions get created by any given musical structure depends on the listener and the context. But what the chromatic scale gives you (compared to the diatonic) is more options in terms of moving the tonal centre around, creating melodic possibilities, and expanding the palette of harmonic colours.