That's not the US system. It is definitely something abused within the US system but to call it the norm is ludicrous: realistically most families can't buy the university a new building (such a "buy in" also is not particularly unique to the US nor uncommon in rich, middle, or low income countries). Most people get in based on merits, but merits are fuzzy and incredibly difficult to measure. All measures of merits can be exploited and hacked as measures are only ever a guide(see Goodhart). Pure meritocracy doesn't exist because it cannot exist. You don't get closer to that meritocratic goal by setting up more bottlenecks or strict standards, but rather by recognizing the chaos and messiness of the real world: that measurements come with noise. You should have measurement, but it needs to be deeply ingrained that measurements are noisy.

> nationwide exams do approach it more than other alternatives

Single-shot standardized exams are well documented at not working. It's a top-down call for a commoditised body of knowledge expressed through a skill that can and is gamed. It's illusory because you could get approximately the same results with a random-number memorization contest or board game. It's an artificial bottleneck designed to filter, almost nothing more. (In fact, by forcing this commoditization you starve the labour force of chance at meaningful early differentiation.)

You tend to find these tests deployed and celebrated in systems with a decidedly non-meritocratic political core, in large part to distract from the fact that the rulers' kids' scores don't matter.

I say this, by the way, as someone who excels at tests.