Exactly!...This idea of playing by ear vs playing written music is a false dichotomy. If one pays attention to the sounds one makes, then it’s no different reading a part or improvising. But you have to pay attention. And you have to work at it....
Here's something I do all the time.
There's a lead sheet in front of me, notes and chord symbols, and it's in a key different than what we're playing the tune in. Bandleader counts the tune off, I start playing it, transposing at sight. Full chorus through, melody exactly as written. Next few guys take -say - six choruses; and during those choruses I make up background riffs here and there. Sometimes they're just variations on the melody; sometimes they're based on the chords written above the staff (which I'm transposing at sight for the first couple times through, but then after that I'm not looking at the music, I'm continuing to play backgrounds while I watch the bandleader to find out when my solo's starting). Then my solo comes up. First chorus I base on the melody, glancing at it off and on to refresh my memory, but introducing ornamentations and deviations both rhythmic and melodic. Second chorus I look at the chords (transposing them as I go to the correct key) and play lines that are completely separated from the melody. Third chorus I shut my eyes and play a chorus of mostly repetitive highly rhythmic figures, ending with a bunch of high notes. Then the drummer takes four, and we all play the last four bars of the tune and hit a chord where each of us chooses a note based on what we were playing during the tune.
None of this is exotic, I'm no fantastic musical genius, I could write down two dozen names of guys right now who do it better than me and not a one of them a full time professional musician.
Now tell me which part of this is "eye" and which part of it is "ear" playing?
False dichotomy. It's all the same thing. You approach each instant in playing music with a constantly varying set of inputs.
Do you really think that the bass players in the pit for Carmen are assiduously staring at each individual quarter note as they play "wump, wump, wump, wump" all through the Toreador Song? Ha ha. They're trying to see if they can see up the soprano's dress.
