I would say a couple of the bands that I like but consider fairly souless are Steely Dan and Yes. Both bands have incredible musicians and create arrangements that are mind blowing, but never seem to scream out to me from the soul. A funny quote from Johnny Rotten from the Sex Pistols that I heard one time was "they (bands like Yes, and Emerson Lake and Palmer) act like they are so sophisticated when really all they are are a bunch of college graduates twanging and bashing slowly and miserably!" It doesn't totally make sense but it rolls off the tongue pretty well.
As far as white bands/musicians that aren't really considered to be "blues" or "soul" music but still have soul and great dynamic intensity in my opinion are the Doors and Neil Young. There are many other examples that I could give of bands on both sides of the soul and souless spectrum, but this is just my mind wandering at 4:30 in the morning, and I don't feel like elaborating. I'll let these cuts do my elaborating for me. Good but souless..."Peg" by Steely Dan. Great and soulful..."When the Music's Over" by the Doors, especially live. I think maybe I'll talk about Bands that are great live but not in the studio and vise versa sometime, but not now. Gotta go.