Is there any other culture in the world where you are "not supposed to" study for an important exam?
The clubs thing is ridiculous too. If my "natural" selection of clubs makes my admission to good school less likely, it is my natural response to adjust clubs selection. The ridiculous thing is basing admissions on fluff like that.
So instead there's tons of handwaving about how the most important predictor of success in life and in education is experience in the sailing club and the polo club and the chess club. Not because its true, but because mostly rich white kids are in those clubs so if you select those groups you'll get the "right" people wrt race and income.
The problem is someone fakes their social life and interests to get into school, if they make it they're going to be surrounded by a weird mix of genuine upper class kids who really did grow up enjoying sailing and playing polo, and a subgroup (perhaps too small to be self sustaining and supportive) of poseurs who don't care about that stuff other than a means to an end.
There is an analogy in software hiring practices. Obviously everyone knows from studies that higher IQ people are more successful. But implementing IQ tests is a legal minefield. Smart people can learn algos. So google does or used to torture applicants with algo questions. They're not looking for people who know all about red black trees or implying that all jobs there use algos, but are selecting people who passed the "IQ test that isn't an illegal IQ test" filter. "cargo cult" copycat companies who do almost the same but miss the intelligence test part, perhaps by asking brainteasers or similar tasks that don't require intelligence, are comical.
The moral of the story, is if you want to do something wrong or immoral or highly politically incorrect, you can get about the same outcome by playing games with overlapping venn diagrams and pretend that a right, moral, popular activity with a large overlap is what you "really" want. A large part of adult/older human cultural interaction is understanding when someone's talking exoterically or esoterically in order to respond correctly.
You're not supposed to prep for standardized tests, either. They're trying to function like IQ tests - a measure of who you are and your education as a whole, not how you studied. ACT and College Board have a wealth of data available, and have concluded that engaging in prep activities between sittings moves your score by at most a few points.
Of course, once it's a social expectation that children of elite parents will go to elite schools, they're willing to throw money at gaming the system. Though a natural consequence of the free market, it still feels distasteful.
Providing these sorts of services freely or cheaply as a charitable organization trying to help rural kids/new immigrant families get on their feet is one thing; charging many hundreds of dollars per hour to a clientele of investment bankers who need to impress their colleagues with their children's admissions is different.