Over the years, I have had students who could not read music but who could sit down and play tunes without
knowing anything about the reading and writing of music. This is a gift and is not learned.
To be honest, I marvel at these skills and support anyone who takes this approach. At the same time, playing the piano from written music opens a far more expansive universe of possibilities. There are tens of thousands of written piano selections out there, and learning to play from music broadens every pianist's world.
Most of the time, I can help a student who plays by ear to also learn to read music – but only if that is his or her goal. My skill lies in teaching piano just this way, not teaching to play better by ear.
I suggest that every student be honest about aims. If you have some natural skills and talent for playing by ear, it can be slow and tedious at first to learn to play from sheet music. But for those with the patience, I can guarantee years of satisfaction to come. It's more than worth the effort!