Let me get some things straight.
When I talk about jazz I think of bebob.
Also, when I talk about jazz I see a trio, drums, bass and a solist. Nothing more, and no chords being played, only implied. (I do like piano in jazz music but for me the need for a pianist is a weakness on part of the solist and the piano is a terrible solo instrument. No expression possible.)
Surely music is at its strongest when it is abstract. I couldn't imagine it not being. I find non-abstract music a comprimise. Something for people who don't appreciate music for the sake of music alone.
Jazz is always improvised.
So yeah, I listen to jazz with those blurrs of notes where the chords are followed and the harmony is created by the solist only by putting the right notes at precisely the right time but with a lot more happening in terms of melody and rhythm.