I think the other posters are right; it's an added expense for parents and a zero sum game. It's in nobody's interest to allow this to continue.
The government should be able to provide enough education to anyone who needs it. But to do that they need many teachers. Somebody must educate the teachers. More learning overall grows the intellectual capacity of the whole nation, it is not a zero-sum game.
I seriously think this is about Chinese Government not wanting its population to be educated in Western values.
Which is a zero sum game.
The solution then would not be to forbid the cram-schools, but the universities which apply that kinds of bad acceptance criteria. No?
I'd actually guess that a ban on for-profit tutoring is a larger risk for the CCP. Students spending their time unsupervised could lead to more "unwanted though" than students spending their time memorizing and reasoning around well-vetted facts about how governments work or about the history of Confucianism.
The students at these "academies" are not being given a robust education in mathematics, science, philosophy or the languages - let alone Western values.
They are rote-learning an extremely narrow type of problem that appears on the gaokao (university entrance exam) - literally hundreds of the same type of exam questions over and over in order to gain an advantage over their peers (hence the "zero-sum" comment).
This comes at the expense of their mental health as well as other, more enriching (and idealogically dangerous!) activities such as socialising with their friends, helping their family with household duties or engaging in rich discussions online.
You could draw a long bow and argue that this stabilises the CCP's power by reducing the drive to protest of angry students who have not been accepted into the universities of their choice, but it has nothing to do with suppressing education or intellectual value.
Sounds like the problem is with the gatekeeping exam and limited amount of good quality universities(aka money problem).
How does banning a practice reduce students stress? They still have to compete in order to get into these limited seat universities with the same exam that you say are easily game-able.
I highly doubt people will just ignore a path that exists that can get them there, so we will have to wait and see what happens with the parents' economic stress.
You people can really spin anything China related to a conspiracy. The Cold War propaganda machine has worked really well. Get a grip.