Consider this - your piano teacher is probably among the best educated person, that you ever met. What other field of endeavor starts when the person is a child? Ever considered it? I had my first piano exam when I was 9 years old! So not only does your piano teacher have many years studying as a child, but then as they get older, they start getting involved in accompanying, and then have music in college, and continue to learn to teach as well as hone their musical skills as they get older. A good teacher is not only teaching, but always learning as well, honing their skills, taking master classes. They are able to play professionally. This all takes time. Don't just look at rates when looking for a teacher. Does the child or you, click with the teacher? Is it someone you want to spend time with? Is it someone you can really learn from? Is it someone who is excited about what they are doing? Are they certified?
So thank your music teacher for helping you to become the best you can be, and realize there is a LOT more behind the scenes than what appears.