Biggest problem is you'd need to make the entrance exams _actually tough_. Like "basically nobody who takes it gets an A". The objective is to rank students between each other, after all! It doesn't matter if the top scorer only has a 70% or something.
Every argument against standardized testing in this kind of thing seems to boil down to "test results are heavily correlated to socio-economic status". But... every other form of university entrance criteria process is even more correlated, right? All those extracurriculars aren't free after all.