I very much agree @bacchist. Life is far more a matter of luck than our egos like to suppose.
However, I would push back on want point you make: That the luck factor makes differences in wealth and income inequality less "justifiable". I agree in part and disagree in part.
If you've never read Nassim Taleb's books The Black Swan and AntiFragile, I strongly recommend them. They go to great lengths to show that most life's outcomes are far more random than we suppose--and that we regularly rationalize away this randomness via after-the-fact explanations that make it "seem" like people "earned" their reward for innovation. One possible takeaway from this is that, since nobody "earns" their reward, there's no basis for large variations in rewards.
But Taleb contends otherwise using market-based economies and centrally planned economies as an example. Let's suppose, that some innovation that really benefits human society--like the glue used by Post-It Notes, for example--was discovered as a matter of "luck" rather than true innovation (and, actually, it was, and frankly most great innovations were). In which economy would the Post-It Note most likely be stumbled upon--a market-based economy where risk taking and experimentation is rewarded financially, or a centrally planned one where a few decision makers at the top direct the efforts of everyone below? Obviously, the latter. The market economy is decentralized, or "open source". Consequently, more people are "rolling the dice". More people rolling more dices increases the odds of one of them hitting jackpot. And when they do, they gain an outsized benefit, but all of society benefits also.
Take away the reward for risk taking and experimenting, as centrally planned economies do, and innovation slows to a crawl.
The word entrepreneur means simply "risk taker". And it's that risk taking that decentralized, market-based systems reward. It's not the discovery or the "creation" of the innovation itself--for that was mostly a matter of dumb luck.
The Steem system actually works the same way. Rewards for the most popular posts are "outsized". Because they are outsized, they encourage people to strive for them--they encourage posting and creativity, for example. They encourage people to take time to write quality content (by which I mean content that they think users will want to see).
But the Steem "winners" didn't "earn" their reward at the end of the day. Most of their winning was a function of "luck"--the right whale happened to subtle upon their post and upvote it at a convenient moment, causing others to see it and upvote it also. And yet, if beacause of that we developed a more "equal" distribution of Steem rewards, we'd actually see posting and innovation and effort decline precipitously.
I don't really find this a compelling argument at all.
Entrepreneur is not simply a "risk taker." It is a very specific sort of risk taking that we consider entrepreneurial. Specifically it is the risk taking of a person with capital or access to capital.
Construction workers take very real risks every day by showing up to work. They risk bodily injury or death in many cases. But his sort of risk taking isn't called entrepreneurship and the market system certainly isn't offering them outsized rewards for their risk.
I don't think it's possible to have an honest discussion about the merits of a capitalist market system without acknowledging the role of class.
I also reject the idea that the only alternative to a profit-driven market economy is central planning, but that's probably beyond the scope of this conversation...