Children's interests can be fickle. Learning a skill takes a serious investment of time, and a child left totally to their own devices could end up bailing on a lot of interests prematurely, because they never get over the initial hump. This is a natural part of parenting, to teach your children about investment of effort.

The horror cases like GP's "9 years" are essentially a miscalibration, failing to recognize a suitable stopping point.

"Cheap babysitting" is not it. Lessons are short and more expensive than childcare. Enforcement of practice time is a hassle (and a balancing act!)

Parental cargo culting, probably. "It makes you smarter" (tenuous, as hinted in article), "all the other parents are doing it to their children"/"I want my child to be better than theirs" (this can be very cultural), "it looks good on your college applications" (this becomes a reason later on, and is also very tenuous), etc.

Status seeking behavior and Narcissism. They are more concerned over their children making them look good to other parents / people than their kid enjoying themselves.