That argument makes sense if your question is what are the odds a specific person becomes a billionaire through sheer luck, but the real question is would a population of billions of people worldwide produce billionaires even if the process of becoming a billionaire involved randomly succeeding a number of times in a row.
The answer is yes for surprisingly unlikely outcomes for any particular individual. Using your coin flipping example, assume everyone in the US was flipping a coin a number of times in a row and the billionaire winners were those who got all heads. It would take ~20 coin flips per person to produce the actual number of American billionaires. Clearly the chance of any specific individual flipping a coin 20 times and getting heads all 20 times is ridiculously small, but there are a lot of people in the US and math is math. Should we ask what special qualities those all heads people possess? Allow them outsized influence in how our country runs and how we live our lives?
The answer is yes for surprisingly unlikely outcomes for any particular individual. Using your coin flipping example, assume everyone in the US was flipping a coin a number of times in a row and the billionaire winners were those who got all heads. It would take ~20 coin flips per person to produce the actual number of American billionaires. Clearly the chance of any specific individual flipping a coin 20 times and getting heads all 20 times is ridiculously small, but there are a lot of people in the US and math is math. Should we ask what special qualities those all heads people possess? Allow them outsized influence in how our country runs and how we live our lives?