lol
I live in Ireland. The authority isn't anonymous, however it is a black box as far as the universities/students are concerned. Students submit their course choices, in order of preference, to the authority. The colleges submit the number of places they have available. Then using that, the authority allocates places to people based on their choices and their grades. If, say, there are 20 places in one course, and 25 apply, the best 20 are taken. The minimum grades of the "worst" person accepted represents the cut-off point - the number of "points" required to do the course. If more than one person are tied for the final place, then it's a lottery. The authority is called the CAO..it's not anonymous, but it's entirely independent. If you are fresh out of school, money won't buy you a place ahead of someone with better grades than you. Simple as that. As a "mature" student, you can apply for courses, and pay the full fees, but you will have to sit exams, and will be held to the standards of incoming students (so in that sense, you can buy your way in..to a degree..but only after having done another qualification etc.). Oh, and there are a couple of private colleges for people who don't make it in the "points race", but with them, you are paying thousands a year for qualifications that aren't so well recognised - employers know that the people who go to these places, generally speaking, are the people who couldn't succeed on their own merits.
$1m per professor? That's simply ridiculous. You could pay far less, and still pay more than anywhere else in the world.