My Latin American State university had a nice solution: a 1 year long introductory course open to everyone which you had to pass to formally enter the university, similar to a centrally-administered course on SAT exams.

The system ticked most boxes: poor students had a lot more resources to study and pass the exams, and the evaluation was very correlated to how well you would do in the University compared to doing than a single exam. It also served as a nice introduction of how to properly navigate a University environment.

When I did this course I wasn't happy in spending an extra year studying before starting university, but in retrospect this is a better system than anything else I've seen. Additionally, almost failing one of the maths courses was a wake-up call that made me realise that I couldn't just wing exams like I did during High School