Regardless of desires to be wealthy, inequality has a lot more to do with inherited wealth, not the ability to be lucky as an entrepreneur. There are plenty of billionaires (and millionaires, etc) who did nothing but enter the world with the correct surname.
We have hyper-concentration of wealth now. Yet there are new entrants entering billionaire class every year.
There are plenty of billionaires (and millionaires, etc) who did nothing but enter the world with the correct surname.
And there are plenty who did not have the correct surname at birth.
Your proof? Most of the 'new entrants' actually have quite a wealth of already accrued money. For example, Jeff Bezos had a loan from their parents for 300k, which is equivalent to for 15 people's yearly salary