Very similar in the US, actually, although maybe not with quite as large of a private system (although some would like to change this). Very similar problems. I've had friends who work in the US school system who complain about this same issue--that private schools are immune to many problems because they can just pass the buck onto someone else.
The linked piece is very nice, and illustrates the selection bias problem extremely well.
One additional comment I might have is about variance. That is, in the figure with red and blue plots, those means are hiding within-school variance. In data I've seen, what often happens is that the lower-status schools often have more variance in them. So in some ways the problem with selection bias is maybe even worse than what the author suggests, because people not only tend to attribute to schools what was pre-existing, but they also tend to stereotype. E.g., you went to a school on the left side of that figure, so you're lower in ability and/or learning than on the right, even though you might be at the upper end of the distribution of the whole figure. This pertains to vocation too: people tend to assume certain vocations are signals of lower cognitive ability than others, when the reality is that uncertainly only increases for some.
The other thing I might mention is some social benefits to attending selective schools. The author at times seems to imply that "talented people will end up doing well regardless of where they go" somewhat dismissively. I think this was probably unintentional, but I think that's not exactly true in the way that people care about, because the studies that are done are kind of coarse. That is, if you study outcomes, they tend to be things like general income, or terminal degree attained (undergrad, master's, doctoral), or whatever. In that sense, things are fine. But because of social connections, people might not get into the particular job they want, whereas another person is given a free pass, or might be at a state-level position rather than a federal-level position, or whatever. That is, there are real consequences to overlooking selection bias, that have real importance for people, but tend to get fuzzed over in studies because it's difficult to study.