I am curious about something.
What style of music is everyone learning during their "lesson time"?
The only style of music I can think of in which "perfection" is the perceived goal is classical. In just about every other form, be it jazz, blues, gospel, rock, or whatever, there is a certain amount of imperfection that is not only allowed, but desirable. In those styles you are meant to feel the music within you and express it your way, within the basic structure of the piece. And in many cases, you are free to improvise! What is "written" on the page is merely a skeleton upon to hang your own notes.
Even classical music gets "re-interpreted" by every conductor who leads an orchestra.
My point is that I'm not sure how much we should get hung up on "perfect" playing, when playing live should be an organic, almost messy process where you as an individual emerges. It still has to sound like music, and hopefully good music, but I wonder if we aren't shooting ourselves in the proverbial feet by embracing a system of learning in which the only goal is "getting it correct" rather than "making it sound good". Because quite frankly, the two are not always the same thing.
Please understand that I am NOT advocating that we dispense with learning good technique or how music "works". Rather, I am advocating a little less emphasis on treating each piece as if there is one and only one "correct" way to play it, and a little more focus on learning to internalize music and how to express it as an individual. It might take some of the pressure off when playing in front of people. Unless you are playing classical piano I guess...