The question is should tax-payers be on the hook for this? Definitely not.
I'm 100% for free higher education paid by the state. I'm 100% against the current college and school system.
It is absolutely infamous for the amount of fraud and corruption, as well as how far government employees will go to force their kids through the exam. In both senses - preparation, cheating, outright fraud.
Fraud horror stories: https://www.bbc.com/news/world-asia-china-53316895
Preparation horror stories: https://www.nytimes.com/2015/01/04/magazine/inside-a-chinese...
Cheating horror stories: https://time.com/4360968/china-gaokao-examination-university...
Having 5 different options in the private sector + a fallback (the state universities) seems a very desirable outcome compared to that, I must say.