I am not the person you were replying to, but no. However, the person who wins should be the more qualified person based on merit not based on some standard of suffering. Just because you had a harder environment does not mean you are more qualified than someone with an easier environment.
It would be trivial to improve our tests of merit compared to the almost impossible task of testing how well a student would do free from environmental factors.
This has never been the case and will never be the case as long as some people are rich and other are poor. A "standard of suffering" tries to show that. Maybe it's a bad idea, but the current system is extremely bad, so people who dismiss this better come up with a better alternative.
Philip K dick also had a short story called Progeny with a similar theme, but here exploring it from the perspective of psychology.
This is one of the weariest types of hyperbolic strawmanning typically employed in discussions of unequal backgrounds, opportunities, etc.
Literally nobody wishes for this imaginary future you're presenting. Not the comment you're responding to, likely not even the staunchest of activists against social injustice.
The question is, do we see children with potential not being able to utilize it because of happenstance, as a problem? Is it fair that a child from a better-off family is more likely to enter better academic institutions regardless of their merit? Should we not help disadvantaged kids?
Of course you can throw your arms up into the air and say "life isn't fair", and hold people responsible for the situation they were born into - but right now we're having this discussion, and we can make decisions and change these things. What if there's a better way?
(PS: Standardized Adveristy Scores don't exactly sound like the better way though.)
At the point of admission, the merits of our two imaginary college kids are not same, even if they started out "the same". The current system, that only looks at objective test scores, is actually blind to anything but merit. You seem to be making the same strawman mistake you described: No one claims that rich kids can buy their way into elite schools, but rather that they can buy better education along the way.
Because they are your parents and they will have an impact on your life whether you like it or not, right down from the genes you inherit to the kind of people you hang out with. So yes there achievement will have an impact on your opportunities.
What you want can only happen when parents are no longer associated with their children in any way and all children are raised by the State so that everyone can be provided "equal opportunities" and even then the type of genes you inherit will impact your opportunities because although social inequality has been removed, biological inequalities can never be removed.
So no your children or not equal to anybody else's children and yes what you do in life will have an impact on your children's life that's how life works.