The wealth controlled by a startup investor becomes earned income, in your words, when the founder receives pay for their work, in the form of cash or exercised options or whatever else.
To get that earned income, which is derived from wealth but is not the wealth, they have to earn it in the same way the wagies in your first paragraph earned it. The investor (on the board, presumably) has to vote him in as CEO and approve his pay package.
And just as retail customers don’t give their money away for no good reason, neither do investors.