> Unless you think that universities should pick their students by lotteries,

The British Open University (distance learning) has no entrance requirements and still has a good reputation and their graduates are successful in getting well paid jobs.

It would be quite reasonable to use a lottery if the number of applicants exceeds the number of places, those who discover that they are not good enough or are not willing to work hard enough will drop out quite quickly. You just need to dimension the first year teaching capacity a bit higher than subsequent years so that you have enough students left at the end of the first year to fill the subsequent years.