I don't understand your high horse here - either the money goes directly to the university from a private donor, or everyone pays (regardless of whether their kids will ever attend university) so the state can fund the university via taxes. This is basically how America's state universities function - a hybrid of direct state grants, federal grants, tax levies, industry and federal funding for specific schools, and private donors and foundations, plus tuition/ room and board.
Private universities rely on funding that is skewed more toward private and industry donations, with obv government (federal and state) contribution too. But private funding is hugely important in that mix.
The UK idea that a university can be funded basically by student tuition bolstered by government contribution is a failed model that has resulted in entire departments shuttered and some universities facing the cliff edge.
By contrast, American universities that have huge kitties can offer a completely free four years to students whose financial circumstances indicate high need and can also thumb their noses at the likes of trump attempting to dictate subjects studied and interpretations of topics he doesn't agree with. Black history, for instance. Universities that are solidly in the black can continue to offer a vast array of language, humanities, and arts courses, and can fund research even in areas that of no interest to Boeing or GE, etc, because the money is there and they don't have to go begging to keep the philosophy department afloat or keep on paying the world's leading expert in Manx poetry of the 11th century.
The likes of Oxford and Cambridge have only recently decided to admit more students from state school backgrounds, meaning that £££££££££ paid to Eton no longer guarantees your son a spot in PPE. I have seen lots of dismay about that from people posting here - basically bemoaning the loss of Oxbridge cachet and wondering if there are alternatives that offer a chance to party with the right people for three years. How is the elitism any worse than your alleged 'corruption'? Legacy / large donor admissions tend to be well qualified applicants, and the money that gets donated to universities because of strong family associations goes toward the financial aid that means less advantaged students can get a life altering education. It would only be corruption if the admitted students were sub par, which is not the case for the vast majority of very 'advantaged' applicants.
If Australian universities have relied on government funding and have been slow to develop 'alumni relationships' / large endowments, then they have left themselves open to interference in academic freedom by all sorts of interested parties, and have limited their ability to offer disadvantaged students the education that could change their lives and the lives of generations of their descendants.
Universities cannot function independently without the money necessary to maintain the integrity of their academic endeavours. The bottom line is the bottom line here.