One thing we hear about over and over is the "reading" musician who can't improvise or learn by ear. That suggests a shortcoming in that person's musical education, rather than a necessary pitfall of learning by reading. A music teacher who only teaches the student to read, without also developing his/her ear, is doing the student a disservice.

I read, and I play by ear, and I'm happy that I can do both. They are not mutually exclusive; nobody should feel like they have to choose one or the other. But you must train your ears, no matter what else you do. You can become an excellent musician without reading a note; there are plenty of examples out there. But I don't believe you can become a good musican without developing your ear.