I think there is some truth to your position, but I think you may be over blowing the pervasiveness of the problem, especially among serious professional musicians. Or perhaps I was just blessed to play mostly with competent musicians.
A person who only plays what is on the page is more of a musical technician than a musician. I know people like that and they tend to play with great precision and skill, but the music is dull, lifeless, and mechanical because their is no interpretation.
IMHO, the term "musical technician" does not apply to most skilled musicians just because they are reading a classical piece or a jazz lead sheet.
IMHO jazz and classical musicians tend to have different musical priorities and different ways of thinking about music. In my experience classical musicians tend to prioritize tone and phrasing, but they generally don't have any concept about improvising melody on the spot.
Based on the assumptions you have expressed, classical musicians would all play rather mechanically simply because they are reading music. But in my experience, on average the best classically focused musicians can leverage tone, articulation, and phrasing to play a written melody far more expressively than the best jazz musicians.
IMHO this interpretation of melody is really just a different form of improvisation, and it tends to be a top priority for classical musicians. IMHO true jazzers tend to prioritize melodic improvisation and memorization above pretty much everything else, and other aspects of their musicality suffer as a results; especially tone in many instances.
Likewise, just because a person is reading a jazz lead sheet does not mean they are not drawing on their experience and interpreting the page. I do agree that an experienced authentic jazzer should be able to play without the lead sheet as that is really an expectation of jazz culture.
I have quite a bit of experience playing jazz, but I do not consider myself an authentic jazz musician. I would also say that I play jazz at a much higher level than most classical specialists, but that's not saying much. I also play classical at a much higher level than most jazz specialists, which is also not saying much
.I am reasonably confident that memorizing a tune would not magically allow me to play jazz at the same level that you do. In fact there are several standards in the Real Book that I could probably still play from memory, even though I prefer having the page in front of me. I feel playing jazz standards from memory is very limiting personally, because all of my mental focus must be placed on keeping my place instead of interpreting the music and playing freely using my normal mental processes. If my goal was to be an authentic jazz musician, I would try to push past the discomfort. But I am more of a jack of all trades and enjoy playing classical, funk, rock, jazz, etc rather than specializing. I am not sure I have the natural aptitude to memorize and hold a bunch of jazz standards in my head, but I do work on it a bit.
I've known many musicians who put significant effort into trying to memorize and maintain the Real Book repertoire, with very limited success. You never see the cats who can do it working on it. So I suspect natural ability is a significant factor that should not be discounted.
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