BTW, I hear boatloads of counterpoint in most jazz, just not counterpoint the way it is classically defined, but a different sort.
A core part of jazz is call and response, where two or more musicians have a sort of conversation in music. One plays a phrase, another replies to it, maybe identical, maybe altered a little, maybe inverted, maybe a different melody but an identical rhythm. That perhaps is pretty much the essence of counterpoint.
Anyone not directly involved in the direct conversation will be playing harmonies in some form, quite likely purely from the defined chords, which is one reason why the chords are often relatively complex. And those harmonies will also have a counterpoint-ish flavour to them.
New Orleans style highlights that well.