Exactly, the universities are extremely wealthy and could in principle choose to use that money to increase intake, but then it dilutes their status as a luxury

Exactly, the universities are extremely wealthy and could in principle choose to use that money to increase intake, but then it dilutes their status as a luxury brand, so they don't do it. But what business is it of the university to be a luxury brand anyway? They should be simply maximising the public good, and that means taking way more students with the huge endowments they have.