Reading is a necessity if you work studio sessions. That being said, much work is based on uncharted (read "very fast") variations on the lead line.
A word of caution: I sometimes prepare a "cheat-sheet", either electronic or paper. If I don't throw the card away after the first couple of performances, that damn card will get yellow and fall apart many years later, without m ever learning it.
Reading is GREAT, but it's a tool, not a clutch.
The head of the jazz department at the University of Kentucky tried to get a job at the club where I did a duo with a drummer (on B-3).
He pulled out his charts. I called a tune he didn't have. IO sent him home.
R.