There are so many reasons that parents choose to pay for music lessons for their children, and they often have nothing to do with the music itself. Often, the parents hope music will help their child academically or help them get a scholarship. If your child doesn't enjoy playing an instrument, they won't stand out. They might be technically good at it, but their performance will lack the qualities that make great musicians if their heart isn't in it.
Besides, there really isn't any financial benefit in the music scholarships offered to students who aren't majoring in music. These scholarships aren't intended to encourage you to choose this school over that one the way sports scholarships are. The purpose of a music scholarship is to fill spots in a band or orchestra because there often aren't enough music majors at a public university to support large ensembles. In other words, the school provides these scholarships as an incentive for students who have already been accepted to participate in these ensembles, and they don't need to make that incentive large enough to compete with other universities.