It's not even about vocalizing it. You yourself could also feel that way... Always questioning if you really earned this. Leading to imposter syndrome, insecurity and so on which might really turn you into a bad leader.
Imposter syndrome is real. But if you are literally on the board of a company, I doubt it matters as much. Also, lots of people inherited rather than earned their wealth. Should we outlaw that to save them from imposter syndrome?
>That kid when he grows up might indeed feel weird about all the undeserved money...
Are you serious? How is taking money from one person who never worked for it and giving it to another person who never worked for it going to make one feel self-conscious and sympathetic to the other?
There are people who refused lottery winnings... Minds are different and weird.
Edit: To directly answer your question, It's not about being sympathetic to the other. They just didn't deserve the money. You "feel" they envy of other people and ask yourself why you and not somebody else. At least if you were the legitimate heir you knew that your family earned it somehow...