Can't I just play without worrying about performance?

Life is a performance art.

"Practicing, on the other hand, is a natural concept.
Animals practice their skills while growing up.
Children practice all the time prior to school.
However, children only practice naturally what interests them.

Children naturally practice sports because they are interested in improving their performance for next time.

Performance tests are real tests, one that natural learners work towards if the task itself interests them. "

From Roger Shank at Engines for Education

I agree with Roger Shank's statement.

Music is a performance art, and the goal of performing should direct all efforts at and methods of learning music and the instrument.

Ballet at Tivoli Gardens in Copenhagen - Photo by Peter Inglis.

Performance is the lodestone, the compass. A teacher will often hear the objection: "... but I don't want to be a performer, I only do this for relaxation." Life is a performance art - there is no escape from that, even with this sort of wishful thinking.

Going to the laundry or supermarket can be a traumatising experience for people who are having problems with their functioning. There is nothing unique about the fears some experience when trying to communicate with others via a musical instrument. The fears are one and the same.

"... the fears some experience when trying to communicate with others... "

And the solutions are the same. That is why dancing, playing, singing and acting are called performing arts, rather than theoretical arts. They are mankind's most excellent and refined vehicle for developing the self - IF - the study and practice are aimed at communicating with your fellow humans - performing.