Bad analogy. Money is representative of externalities, of things exchanged by others, like the time they spent working to earn the income, or selling something, and it extends through many levels of transactions in society.
That’s nothing like someone’s good looks, which, by the way, is subjective and has changed over the ages.
Using this logic, having good genes represents an even greater injustice.
As you have said, money is a fuzzy representation of at least some value created via societal transactions.
Genetics, on the other hand, are wholly undeserved, even by the people passing them on. If we aim to champion fairness, I don't see how this cannot be part of the conversation.
We should do plastic surgery to the best looking children to make them average-looking...it's social justice.
We won't achieve true fairness until we forcibly take central control of all decentralized processes (markets, nature) to ensure no tall poppies.