Having been a trumpet player, I can read the right hand parts fluently. I can follow the left hand parts if they are simple, but I play left hand chords 100% of the time and let the arranger to the work.
Having said this, I rarely read anything anymore; I just listen, find the chords, and improvise. I can hear melody lines and most of the time play them without much struggle, particularly in the keys where I am most comfortable--C,F,G,D,A,Bb,E--in that order. One of those keys will suit my vocal range on any song I want to do. If not, push the transpose button.
In think "playing by ear" is somewhat a misnomer. What most of us do is understand the chord structure and the way the chords and lead/fills interact.