My daughter didn't enroll in a local drama school, but she did join her school's drama club. They met for an hour or so after school, so I'd have to pick her up on my way home from work. She got over a lot of her shyness during her three years in the club, and actually got to participate in community and college theater productions. She did get tired of it after a while, however, and became more of a musician.
I'd say parents should allow their children to pursue drama classes, but they should realize that many children move from one interest to another. Only a small percentage of children ever decide to pursue acting as a career.