The fact that there are a bunch of asian kids from poor socioeconomic backgrounds who make it into stuyvesant https://www.refinery29.com/en-us/2019/05/233354/stuyvesant-a... is one example of how standardized testing can make it so that hard work can make the difference. I'm not saying that rich kids don't have an automatic leg up, but that's always going to be true regardless. Standardized testing (if anything) gives everyone a shot.
Realistically, it's much easier for a person of average means to study for a standardized test than it is to buy the transport necessary to an international math/science/business/water polo competition.
It's fundamentally impossible for a person to do well in ice hockey if they cannot afford the hundreds of dollars in skates and protective equipment needed to play the game. Taking a standardized test is usually free. Does money give an advantage in both scenarios? Yes, but at least it's not an absolute barrier in the second.
So all mediocre kids with money have better chance than a brighter kid who couldn't afford coaching. Of course genius could still make it through this system but genius can also make it thru school grading system. There are enough programs to help out them.
Problem here is that barely above average students who wouldn't want to study all subjects per curriculum start to think of themselves as ignored geniuses crushed by the system.