The algorithm didn't keep the gap between paid and unpaid education, it expanded it.
(Source for these numbers and more in my first comment.)
I was lucky enough to not only go to two private schools, but the second one was ranked #1 in England for exam ranks 2 of the 3 years I was there (and helped me get good grades despite being extremely unmotivated and lazy). But at least my privilege was to be given a good education that made learning / passing exams (the latter more) easy, not that the government decided my school deserved an artificial grades boost compared to state schools.