https://www.theedadvocate.org/9-benefits-music-lessons/ says:

Has your child been asking for lessons on the piano, the guitar, or maybe even the saxophone?

If you’re hesitating about the commitment, here are some great benefits for kids who learn to play a musical instrument.

1. It builds language skills. As they learn their instrument, children become accustomed to different sounds that they would not have recognized before. This practice trains their ears for the nuances and subtle sounds of language.
2. It makes them stronger academically. Researchers have found connections between music lessons and nearly every measure of academic achievement: SAT scores, high school GPA, reading comprehension, and math skills. Music also improves their powers of recall for powerful learning in all subjects.
3. It increases their IQ. Numerous studies (including this one in 2004 by E. Glenn Schellenberg) have proven that children’s IQs increase because of even a few weeks of music lessons. Brain scan technology reveals that brain activity increases following musical training, and some parts of the brain even grow larger!
4. It teaches them discipline. Your child may be expecting to become a viral sensation overnight, but in fact, he may have to spend hours even just learning the proper way to hold that violin or trumpet before he can even make a sound. Music lessons require hours of concentration and patience. Children must persevere even when things aren’t going well…an invaluable skill for all areas of life.
5. It supports muscle development and motor skills. Children must use their whole bodies to keep the rhythm going when they play. They also must coordinate different motions with their hands at the same time. In doing so, they develop strength and coordination.
6. It improves social skills. If children play in a group, they have to learn to work together to achieve a common goal, exercising tolerance, patience, and encouragement towards their peers.
7. It makes kids feel good about themselves. There’s nothing quite like the sense of pride that comes from working on building a new skill for an extended period of time…especially when the result is beautiful music.
8. It helps kids understand culture. By learning music from various parts of the globe, students come to understand these cultures, whether it’s African drumming or Argentine tango music.
9. It brings joy. And finally, we come to the most important reason of all. When children can play music, it makes them happy…and everyone else too.

And you thought they were just learning how to play an instrument! Little did you know that your children will accomplish so many other wonderful things too.