Even if music is not pursued as a main interest or hobby your child will benefit from musical training throughout their life.
My experience is taken from my son who is now 13 years old. He started piano lessons when he was 6 years old and did very well and enjoyed them. He did not necessarily excel at it but he did do well. Although he would never sit down and play for the pleasure of it he would always work on his lessons and enjoy playing the songs his instructor assigned.
When he turned 11 his interest level in piano dropped and at the same time his instructor moved and stopped giving lessons. My son wanted to quit and was not all that interested anymore. I encouraged him to stick with it but after 6 more months with a different instructor and my son not wanting to practice I decided to let him drop it and move on.
Now he is 13 and his pursuits in math and science are taking the front seat. His musical training will always be with him and I believe the understanding of music helps him in his academic pursuits. He is now becoming interested in playing piano again. If he sticks with it, great, if not then the music skills he learned will enhance his skills in other areas of learning.
When playing a musical instrument many processes of the brain are involved. You have to order things as in: verse, chorus, bridge, verse. You integrate counting into your feel with timing as in 4/4, 3/4, etc. Looking ahead or remembering what is coming next in the music is essential. You listen and use your ears in a thoughtful and directed way. You have to use your hands and arms and …