When I play by ear in front of people, it's a show stopper. They can't beleive that I get all those tones from just my ear lobe.
Many folks that play single noted instruments, read music. But some of them have admitted to me that reading piano music (up to six notes at a time) is over-whelming for them.
Additionally, I would say the majority of music reading musicians that I have encountered, do not know how to improvisate. They are chained to reading music and lack the passion of expression. But there are the exceptions to the rules of coarse.
But one should realize that music is a basic expression of the human heart. There is a lot of value in knowing how to read music and the theory behind it. But music did not start out that way.