Do you mean that the private schools could use social credit scores to select students? That is possible, maybe even likely. But one would think or at least hop

Do you mean that the private schools could use social credit scores to select students? That is possible, maybe even likely. But one would think or at least hope that there will be diversity, as some private schools may then cater to the unmet demands by others. Remember private schools are in the business of competing for both revenue and talents. A "best" private school that refuses to accept the best students may soon find that they are no longer the "best" school anymore. OP was talking about a government ban. I could only find cases of courts enforcing civil judgement this way at some cities.