There's always something to be said for letting the person try what appeals to him or her. I have a long history with music. My sister and I started with the violin (her) and piano (me) at age 6, and we still, in our seventies, play together. But that is because we had good training and good supervision from our parents. My mother sat with us to practice when we were little.
With my own children, (seven), two became accomplished musicians, three professional dancers, two professional visual artists. Everyone wondered how we could possibly have so much talent in one family. The secret is getting your children to actually stick with something long enough to become somewhat proficient. The activity then becomes self-rewarding. My children loved what they did.
Practicing was always done for a half hour before school. That way, it didn't interfere with after school play or sports. If lessons were involved, we didn't cancel to go to the beach or because "but I want to play with my friend today." If we could see that the "fit" for a particular instrument or activity wasn't right for that child, we allowed them to stop after an agreed-upon period of time. That went for dance lessons, ceramics lessons, etc. You had to agree to practice where that was appropriate, go to lessons and pay attention and try your best, and stick with it during the period of instrument rental, or until dance shoes were too small, or art materials were used up -- whatever applied.
In my opinion, most kids drop out because they never receive the training or supervision with practice that allows them to really enjoy what they are doing. No one enjoys doing something badly, and very few people do something well without attention and practice. So your commitment needs to be, whatever the instrument, to supervise practice and pay attention to what is being learned. Usually school instrument practice isnt all that difficult, at least at the beginning. Look over the instructions on how the instrument should be held, what mouth position is correct or hand position is correct, etc. Have the child go over each assignment three times correctly. Then practice is over! The teacher will be grateful, your child will do well, and if the instrument is a good fit, you may have a budding musician on your hands.
I hope this is helpful in some way.
S. Toji