Although I can't fault your picks, I don't really consider members of steady bands - whether operating under the name of their leader or not - to be sidemen. I mean, Keith Richards may write a lot of the songs, but he's on record as saying that if Charie Watts left the band, that would be the end of The Stones (whether that might actually be a good thing at this point is a different question!).
Even in a case like early Elvis Presley, where he was the only star of the show, I love the work of Scotty Moore, Bill Black, and D.J. Fontana, and consider them to have been integral members of a group, not mere sidemen. To me, to be a true sideman, you must play the field, working with a number of different lead artists. So the Motown guys (calling themselves The Funk Brothers), including the ones you mention plus Earl Van Dyke, Benny Benjamin, and many others, qualify handily.
Same with The Memphis Group (better known as The MG's, with Booker T. Jones, Steve Cropper, Al Jackson, and Duck Dunn or Lewis Steinberg) - the Stax house band with Otis Redding and Sam & Dave plus a ton more (and of course on their own), as well as the Muscle Shoals rhythm section over at Atlantic (Dan Penn, Spooner Oldham, Jimmy Johnson and others) on Aretha's and Wilson Pickett's records to name just a couple.
Getting back to Elvis, he had one of the best playing guitar in his Vegas years, James Burton, who also played for Ricky Nelson's band and many others from the 50's through the 70's (including on the original hit recording of "Suzy Q" by Dale Hawkins when he was about 17 years old). Similarly legendary on guitar is studio (and solo) ace Chet Atkins, who supported many other acts in his roles as producer, arranger, and sideman in between having hit records of his own.
The west coast equivalent of the above-mentioned soul studio bands was the loose L.A. group of studio cats known as "The Wrecking Crew", including the talents of Hal Blaine and Earl Palmer on drums, Carol Kaye on bass, Leon Russell on keys, Glen Campbell and Jerry Cole on guitars, and many others, who played a key part in the delevopment of the California pop sound of the 60's from the Beach Boys to The Mama's and The Papa's and a thousand other hit records in between.
All the cities with their own thriving music scene and recording indutry had their own side groups and players, from New Orleans' Dave Bartholomew group (Fats Domino plus many more) and The Meters (Lee Dorsey plus many more, and as a headlining group), to a bunch of New York jazz cats who made rent playing on rock & roll records during the days.
Probably the best known case of a group of sidemen becoming stars in their own right as a band is, apppropriately enough, The Band, who as we all know started off as the backing group for rockabilly Ronnie Hawkins before playing with Dylan in the mid-60's, and then going their own way with such landmark results.
The arrival of The Beatles as the model for the self-contained rock group made being a sideman an increasingly endangered occupation by the late 60's, though the singer/songwriter proliferation of the 70's brought them a return to demand. After the punk explosion of the later 70's, self-contained groups have again become the norm in the rock industry to date, though there will always be unheralded behind-the-scenes players.
