That's an interesting point. Indeed, I imagine that it is possible to become a great classical virtuoso and sight reader without understanding anything about the harmonic foundation of the music that you are playing. In addition, as the emphasis in classical music played for the general public has shifted from composition to performance, understanding harmony is probably becoming increasingly less important for a successful musical career.
You can't do that in jazz! (At least, you didn't used to be able to do that.

)