When I was younger in my teens, I went to my neighborhood piano teacher, an older lady that went to Juilliard in her youth. The very first thing she had me do is sit down with very elementary sheet music songs, after which I progressed to tougher classical songs. We went through the series 'Piano Pieces for Children' (remember that green book?) and for four years I was working on classical pieces. No theory. No chords. No playing by ear. No choice. Just learning how to read sheet music. The mechanical nature of it made me detest music for many years.
A decade later I started learning guitar with youtube videos and what I liked about the guitar is they emphasized music theory / chords / scales and less sheet music. Also the guitar was more concerned with pop songs and songs on the radio than classical music. It was around that time I saw an infomercial by a guy called Scott Houston who had a series called 'Play Piano in a Flash' where he didn't teach reading yet emphasized teaching theory and just playing piano based on patterns and it just made my jaw drop how easy it was. He had these really long late night informercials.
Anyway, since taking up piano again, I've decided to only stick to theory and playing by ear. there's a great piano teacher called Karen Ramirez that emphasized ear training. I'd watch all her youtube videos. Even she mentioned that piano teachers prefer to teach students how to play sheet music. and that it took her many years to come to the realization that one can play by ear, simply because all her teachers never emphasized that.
Why don't piano teachers teach how to play by ear and theory before they go into sheet music, or at least have the student pick what he or she'd like to do? You can say that there's different types of teachers. but it's not like that, the vast majority teach how to read sheet music. Most people just want to play what they hear on the radio, and it's alot easier to just do that by learning chords/scales and practicing picking out tunes. We are already musically inclined when we are born, most of us can hum and whistle. Same can be done on an instrument. So why introduce sheet music as the first thing when learning an instrument?