Unless you're arguing that a First Lady is totally incapable by definition, that's not what I am arguing. The first Lady can sit down at a desk if she wants and do all the initiatives she wants, just not an Executive Office of the Federal Government. She can open an LLC, she can open a non-profit, she can open a studio, whatever, commute to work (with paid for security), or - should she feel compelled - work from the private apartments of the White House which are de facto private (with some advantages of course). She can hire her staff, on her dime, and be as successful as many other Americans (with the de facto advantage of her being known, but nobody can't do anything about that).
The Office of the First Lady is a full fledged Office of the Executive Branch, with its own staff, its own budget, its own policy director, etc. and fully paid expenses (including air travel) and the right to use Federal areas (White House rooms for example) for various initiatives. It's not just "a desk".