Okay, showing my age here a bit...
My current version of Band In A Box is from 2009, it wasn't all that expensive then, can't remember how much. It took me a long time to figure out how to use it. My version came with a feature called Real Drums, which is comprised of samples. BIAB is definitely geared toward jazz, and the Real Drums include very realistic and very usable brush and stick kits. Although you can't really use BIAB on the fly for accompaniment, it's fairly easy to make some good sounding back tracks which can be exported as midi or audio in separate tracks or combined. And, remember this is with the 2009 version. So, maybe current versions can do even more.
An easier way to get some backing tracks, although more restricted, is with Jamie Abersold's Play-A-Long sets. They are recorded with the drums in the middle, piano on one side, bass on the other, so very easy to use just the bass and drums. Some of the JA stuff suffers from tempos being a little too fast, but most of it is spot on with the original arrangements. His Miles Davis, Jobim, and Count Basie tracks are very good.
Years ago, maybe in the early 90s, I had a neat little thing from Yamaha called QY-20. It was about the size of a VHS tape, had several drum kits, three or four basses, some piano voices, organ, vibes, horns, strings, ran off of midi, had a set of buttons laid out like a keyboard, and was either programmable, or, if I remember correctly, which I might not, could follow left hand chords from a digital keyboard. I also remember a friend who had a Yanaha PSR something or other that would follow left hand chords. Of course, tempo changes had to be changed manually; not exactly AI, but quite usable.
