The top results (for me) all say that it's not literally correct that only 50% of middle school students make it to high school, but most (suspiciously) only mention numbers for Beijing. https://zhuanlan.zhihu.com/p/368135272 has a table covering every province, showing that the rate goes from 53.11% in Henan to 70.49% in Heilongjiang.
It's interesting that there's no calculus on the gaokao. It's an elective in high school (same as the US). I wouldn't have guessed that. However, some very basic linear algebra does seem to be in the compulsory high school math curriculum(1). More than I learned in high school in the US, anyways.
Also, generally the private schools are considered worse options. The elite students with the highest middle school test scores mostly go to public high schools. Maybe students at the private high schools are more likely to go overseas, and so they are more likely to take the calculus electives. But even among the private school students, only a small percentage will go overseas.
For the vocational school thing, I had no idea it was so extensive. Very interesting. I knew about sports high schools, where most of the graduates go on to teacher colleges and become PE teachers. What other kinds of vocational high schools are there? How does it work for smaller cities - how many special types of vocational school can they really support?
(1) https://baike.baidu.com/item/%E9%AB%98%E4%B8%AD%E6%95%B0%E5%...
About calculus: https://www.gaokzx.com/c/201901/33164.html
Using the elite students from private schools who you know as a counter argument is really not that strong. Only 14% of the high school students are in private schools.