Does being a physician require a higher level of emotional intelligence, memory, reasoning, spatial intelligence, determination, stamina, moral conscientiousness, compassion, and a lower amount of mental illness, physical illness?
Not everyone can become a physician. Those who lack in any particular dimension have to compensate in other ways to succeed in medicine. It's why medical school admission is so competitive and multifactorial, to weed out those who can't make it, and shouldn't make it in the case of lack of compassion.
What do physicians deserve for an income? What do basketball and football players deserve? What do CEOs deserve? It's all from the same mindset: someone else has something I do not have.
And yes, the secretary would suddenly have a valuable set of skills that would command more in terms of "wealth".
Generous social safety nets are a compromise between "everyone gets the same because all inequality is wrong" and "If you're not doing something important you should die in poverty".
To the extent that their differing roles are circumstances of birth and life, and that fairness is part of your morality, yes, it is.
> Do they have teenage pregnancy? Do they study hard in high school or trade school or professional school or engineering school? Do they have business intuition to start their own business?
Those are all circumstances of birth, be it nature or nurture.
We have a strange notion of "deserve" in our society, that someone deserves more simply because they have a skill or circumstances that are in lower supply compared to demand. So physician skills are in shorter supply than secretary skills. But if they were shipwrecked on a desert island, and the secretary knows how to fish and keep them alive, suddenly he can command a greater share of income on that island. Arbitrary no?