Perhaps the answer is found by first excluding keyboards that can't do styles, accompaniments and arrangements. Then eliminating those whose styles, breaks, fills, and ends are barely usable. That would meet my criteria for minimum quality arranger.

Which brings me around to software, controlled by a generic MIDI keyboard, with assignable sliders, knobs, and buttons. Any recommendations / caveats with respect to MIDI controllers?
Currently looking at m-Audio and Novation controllers.

Other than Band in a Box, are there any other music programs that replicate the functionality of the arranger keyboard with respect to styles, variations, and accompaniments?

Are there any programs that one can record a melody along with a click track, and have the software determine key, chords and time? Especially, for unusual time signatures?