I think that is one of the reasons, or perhaps the main reason for the success of this session. Yesterday I re-listetened to the first Norman Granz studio jam session with Charlie Parker, Benny Carter, Johnny Hodges etc., and it follows the scheme of the JATP sessions, mostly up tempos, a ballad medley for change of pace, and this leads to a cutting contest stereotype with flashy solos. Oscar Peterson also is a factor with his adaptable but rather formulaic approach with a tendency to display his technical prowess. Jimmy Jones on the Ben Webster And Associates session is totally different from Peterson in all ways.
I just ordered the Harry Eddison album with Webster where Jimmy Rowles is on piano and am curious how much of a difference this makes.
I experienced the same thing when I played in a quartet of a singer backed by piano, bass, and me on percussion. We rehearsed Monk's Straight, No Chaser and it resulted in rather routine blues changes improvisations. So I suggested we change the solo routine: Intro with just walking bass and voice during the first chorus, conga and piano throwing in accents during the second, followed by the fours of voice and piano with the congas. Then the bass solo, then the voice scatting, the piano, and the end theme with the whole band. It worked wonders and during the first gig with this arrangement the bassist played his ass off. We all were alert as we had to pay attention to what comes next.