So you think that someone that can't even begin to comprehend the course material should be allowed in just because they want to go there?
When there are more qualified applicants than available slots, you need to limit the number you admit to supportable levels.
On the other hand, you shouldn't let unqualified people that just don't have the requirements because they can't succeed, and will just be wasting resources, especially when there aren't enough slots for the qualified ones.
In this case, there were no qualified applicants. Do you expect them to repeat grade school & high school math and teach remedial English just so they could admit new 'students'? That's a waste the colleges resources. Colleges and Universities are Advanced or Higher education. If you don't have the lesser ones yet, you can't be taught the next level. It's like trying to build a skyscraper without a foundation. It will fail and topple, wasting a lot of time, effort, and other resources.
So no, I can't agree with your opinion that it's a failure of a university to have an entrance exam. Rather, if it's any ones fault, it's a failure of the prior education system or students that makes an exam necessary.