That is the premise behind those points and the ones raised by the op: Luck is never part of the equation, just ask your average rich guy from rich families.
There is widespread statistical evidence that wealth is gained through luck. I imagine though that every billionaire thinks they are the one that got there through hard work.
I remember another study that looked at people who had made it very rich, and they saw that luck was something like 'being educated in a field just when that field is about to make a huge impact in the world' - in other words, great timing in addition to raw talent. I don't have the link to hand now though.
While I’m not sure I’m following you 100%, luck takes a bigger part the higher the wealth. For example, existing billionaires have a way higher chance of having inherited a huge sum than the average population. If you take sound financial decisions you might get up to a million or a few, and above that it will be always more luck than skills. 100000x that is a huge lot of luck.
One huge thing the 'self-made' vs. 'privileged' classification misses is pure and simple luck.
Two equally competent candidates apply for the same highly selective position, but one of them gets the job and the other doesn't. Two people try their hand at the stock market, but one person buys in right before a recession, and the other buys right before a boom. You can claim that over a lifetime, luck evens out, but I don't think that's really the case -- there are key junctures in every person's life where luck plays a huge factor in their eventual path.
It's supremely hard to disentangle luck from all the other factors, because for every random factor you can always come up with an ex-post rationalization that gives yourself all the credit ('I built a better rapport with the interviewer', etc.), and successful people I've noticed tend to be unusually good at assigning themselves credit.
A classic paper that looks at how wealth is distributed if every time two people randomly interact, the richer one is slightly more likely to gain money [1]. Everything else about individuals is identical. The rich always get richer.
I read something by Richard Branson that said--and I'm paraphrasing--that everyone is given about the same amount of luck. It's all about what we do with the luck when it falls in our lap.
Everything's about luck. Are you smart? Luck. Are you good looking? Luck. Are you rich? Again, some combination of things that are all essentially about luck.
It's not either "just luck" or no luck involved. Sure, most people who do get rich try and work very hard. The question is how big a proportion of people who work hard do get rich. If it is only 1% and it cannot be predicted in advance who it is, then there certainly is an element of luck.
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