This is like saying all furniture must be made waterproof because some people have leaky roofs. No, you fix the roof.
I know my proposition sounds absurd, but it kind of point out the issue with this kind of thinking is that applying some patchwork fixes to complex issues rather than treating the root cause is a bad idea. It's a bad idea in CS and a bad idea in planning social systems.
Neighborhoods should be made safe, or failing that, dorms should be made available for kids (in my country, there are tons of dorms for high schoolers already, who live in the countryside, and want to attend a somewhat better high school).
Alternatively I suggest making this a demand problem - good high schools should compete for talent (which is always in short supply) and should actively take measures to seek out and nurture gifted kids.
As for your rich kid example - what makes you think that in a more holistic system, he won't be able to optimize admissions by exploiting resources?
Just recently there was an article on HN about how the majority of those admitted to US elite college received some 'pity party' points - sounds to me the system is being actively exploited.
Fixing the root problems sounds good to me.
But that doesn't mean that as it currently stands you can say that standardized tests gives everyone the same chance in the US. It would in some hypothetical future maybe yes, but not now.