Ha! This was basically my response to my friend, in different words. Largely because I hear so much church music and blues in Turrentine's playing. (Someone mentioned Fathead - same applies.)
These players are right there in the centre of the continuum that then gets packaged as blues, jazz, gospel, soul, R&B or whatever depending on the target audience and route to market. Who is to say that Ray Charles and Lonnie Johnson aren't jazz, but Jimmy Rushing yelling over Basie or Lester Bowie playing 80s pop is; whilst Louis Jordan either is or isn't, depending on who you're trying to impress?
However, I still don't think that's all of it. These "blues/bop" players emerged from that continuum and were recorded in that style at a specific point in time. Who were the individuals who led the way, or the events (artistic, commercial, personal?) that caused recordings of this sort to be perceived as potentially lucrative and to be released?
Perhaps it was just the effect of Parker re-entering the swing/ mainstream/ blues bloodline as bop became less specialised and more widely diffused, but you'd still expect to be able to point to leaders and milestone records, like you can with Jimmy Smith and the explosion of soul jazz on the organ, or (going much earlier into the same musical continuum) Blind Lemon Jefferson and the growth of unaccompanied guitar blues.