Hard work is very different from skills/talent or luck. The OP is claiming that the rich kid has a different/better personality skill set from the regular kid based on his wealth, and I disagree with that. I believe the rich kid has more opportunities, yes, but I don't believe rich kids are bred to have a better personality to take advantage of those opportunities. Therefore, it falls upon our society which looks at other factors instead of valuing merit for merit's sake.
Let's assume the two kids are just as driven as each other, with the rich kids having more opportunities. I do not believe that the rich kid will always have the social skills, technical skills, brains, passion, or dedication to take advantage of those opportunities. The rich kid may be a very mediocre person by merit, but because the regular kid doesn't have access to these opportunities, our society will select the rich kid for this opportunity because he looks good on paper and for lack of other merited kids to pick from. So yes, the rich kid will be ahead PURELY because he had exclusive access to an opportunity or because society wanted to pick a better resume, but NOT because the rich kid has a better skill set or is more well adjusted than the regular kid based on their wealth backgrounds. This disproves the OP's point.
I'm not sure you've really disproved anybody's point.
Consider that a rich kid's parents will likely spend hundreds of thousands of dollars (if not more) on their child's education, on everything from the best preschools to a top prep school to an Ivy League university. Do you really think those schools offer nothing in exchange for all that money, aside from some better social connections and big names on someone's resume?
It's very, very difficult to reduce the impact of a lifetime of educational and social advantages down to something like "different/better personality skill set," and I think in doing so you are woefully underestimating what kind of benefits those advantages bring.
I'm not underestimating the benefits of those advantages at all. But those are opportunities bought with money. I know plenty of my peers from Ivy League schools who had the personality/skills to take advantage of everything their private schools and Ivy League upbringing had to offer - studying abroad, discussing with the best professors, etc. But I also know plenty from this same group of peers who have had access to these opportunities but are still softspoken and shy, or nervous when speaking with people, or have insecurity issues, or are elitist snobs who turn people off, so on and so forth. Sure, maybe they took Calculus in high school and have a PHD in whatever metaphysics but does that mean they are better adjusted to take advantage of all the opportunities that money has bought them? In fact, if you have 2 kids, one rich and one average, the rich one being socially ill-adjusted (because his parents were hyper-ambitious) and the average kid being happy-go-lucky, smart, and resourceful (because his parents nurtured his childhood with love and taught him the skills of problem solving and confidence), assuming they had the same opportunities, which do you think would do better in an interview? Obviously I'd like the say the latter, but that then brings up the point of whether society values the better resume and lesser merit or vice versamore.
Let's assume the two kids are just as driven as each other, with the rich kids having more opportunities. I do not believe that the rich kid will always have the social skills, technical skills, brains, passion, or dedication to take advantage of those opportunities. The rich kid may be a very mediocre person by merit, but because the regular kid doesn't have access to these opportunities, our society will select the rich kid for this opportunity because he looks good on paper and for lack of other merited kids to pick from. So yes, the rich kid will be ahead PURELY because he had exclusive access to an opportunity or because society wanted to pick a better resume, but NOT because the rich kid has a better skill set or is more well adjusted than the regular kid based on their wealth backgrounds. This disproves the OP's point.