There are about 200 thousand universities in the world. All of them compete for attracting applicants. Different applicants. Harvard, MIT, Oxford, and other most prestigious universities are fighting for the best applicants, while the vast majority of universities need at least some applicants.
How can a university increase its chances in this matter? The answer is to look at the situation through the eyes of potential applicants. What is important to them? First of all, the quality of education, you say. But the more prestigious the university, the higher (as a rule) the tuition fees. The best option is the university with the highest ratio "price: quality." As far as I know, Australian universities are by far the best in this respect. However, they have a significant drawback: they are located too far from the rest of the world. American education, in my opinion, is too overrated.
And which university would you like to enrol in if you were 18-20 years old?