I think you're still misunderstanding how the private tuition works.
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.