In recent history, First Ladies have effectively acted as members of the President's team to advance American interests, sometimes even attending events on the President's behalf. But, the First Lady doesn't earn a salary for her work. Is this different than spouses who make sacrifices to help advance the careers of their partners without pay?
While her specific duties aren't delineated, matters of state wouldn't be conducted in the same way if she were to continue her own career outside of the White House. And due to the conflicts of interest that'd create, it's not a realistic choice.
If she chooses to work as head of the Office of the First Lady with a salaried staff that's part of the Executive Office of the President, it only seems fair that she be compensated like other members of the President's team.
* PS I wonder whether people's perceptions would be different if this were about the First Gentleman instead.