I wonder if most sax players belong in the blues/jazz genre. Of course you can find them in classical music, as well as rock bands etc...but mostly jazz?
In the book "Crosstown Traffic" which is sort of a biography of Hendrix but more a exploration of American music, the author Charles Shaar Murray points out that the sax as soloist in rock and roll died out in the late fifties/early sixties due to better amps, more adventurous sound processing and ease of transport of guitar. In jazz, for a variety of reasons, people weren't looking for the sort of guitar sounds found in rock or blues and with notable exceptions, guitarists weren't the featured players.
"The Blues Brothers" soundtrack is loaded with sax, but are these famous songs really blues? pure blues?
It depends on how you look at it I guess.
The original versions were generally not considered blues by young people in the sixties, but Booker T &The MG's and Muscle Shoals/Fame were accomplished blues musicians. Many of those songs have bluesy elements. Otis Redding could sing blues but was not a blues singer. Am I making sense?
Anyway classic Chicago blues bands rarely had horn sections until post-James Brown. But Texas blues bands ALWAYS had horns and prominent keyboards. Albert Collins rarely recorded without at least two sax players. Coming out of Memphis BB kept horns in his bands even when he wasn't making much money.
And I didn't mention Nat King Cole in my first post even tho I listen to his albums every now and then. Guess I never really thought of it as jazz music, despite the piano.
(do) "Unforgettable" or "Mona Lisa" belong in this thread?
I'd say so, Fame. I can't find it now but I seem to remember a recent (past 6 months) NYT article that pointed out that although Cole was primarily known as a smooth crooner, he was actually a pretty fierce pianist-among the best. The author was writing something like how unfair it was that someone could be that skilled at two different things. If you go back and listen to Cole, Charles Brown and Ray Charles, there's not a lot of difference.
I don't think it was
this article but if it wasn't it was very close.
On some of these things it would be like debating exactly where does red turn into orange or where does blue turn into indigo.

As long as you're in the general vicinity, and not trying to say red is violet

it's all good.