So these expensive prep schools have two enormous problems:
First is that they make the cost of education too high, thus reducing the amount of people who are willing to have multiple children. And the reason that the cost is high is because these schools promise vast improvements in test scores making it nearly impossible for children who don't take these classes to compete with those who do. In that way, parents have no choice but to pay and everyone would rather have one prodigy kid than 2 or 3 who are mid-low tier in their classes.
The second issue stems from the first issue and that is that in order to produce these massive improvements in their scores that convince parents to hand over the big money, (over kids who already study the material very hard on their own, not over kids who don't study,) is to focus on teaching them skills that crack tests but are useless everywhere else. (Ex. Just look at the answer choices without the question, and use the differences amongst them to psychologically determine how the test-maker tried to trick you and where he hid the right answer.) This produces kids like my ex roommate, who scored a whopping 750 points (high 99th percentile) on the English section of the GRE, but ended up virtually unable to communicate in English, having difficulting understanding classes in the US and needing native English speakers to proof his disastrous essays when those people really only scored in the 500's (~70th percentile), sometimes even 400's.
The final combined effect is that parents reduce the number of children they have in order to raise kids who don't know how to do shit except find the correct multiple choice answers on a test without even trying to understand the questions. Needless to say, that's not good for China.
By making these prep classes non-profit, they can't charge egregious sums anymore and they lose the motivation to train kids on useless skills that elevate their scores without adding to their knowledge. This kills 2 birds with one stone; the parents now have more money and can consider more children, and the kids actually study the subject rather than test-maker psychology.