Being FLOTUS reflects who you are as a person. Regardless of being “unpaid” the role does come with nice benefits -paid staff, arbiter of all things related to entertainment and probably wardrobe. But it is a "traditional’ female role - beautified, nurturer, kindly, selfless, caring.
Since it has never been a male, we have kept these expectations one I believe.
However for each administration, the traditionally female role as FLOTUS reflects who they are individually. Less memorable -Pat Nixon, Mamie Eisenhower, Bette Ford, Rosylyn Carter, and Laura Bush.- who were less outgoing and/or sure of themselves. Issues about drinking and breast cancer were put into the national spotlight though.
For this FLOTUS group - Eleanor Roosevelt, Jackie Kennedy, Nancy Reagan, Barbara Bush, Hillary Clinton, and Michelle Obama -they exuded way more savvy about their jobs. They empathized better, steered people into literacy, better health, the arts and were more combative. Traditional yes, and forces to be reckoned with for sure. Not sure if Nancy Reagan’s message was anything but tone deaf (Just say No) but she acted from strength and presented Reagan well.
But if you are asking is FLOTUS really doing a job…? More than anything, I believe they help shape the moral fiber of the country. Ie., Helping others, reading helps you learn, eating healthy food makes for a healthy life (and nation), HIgher education gives you more opportunities and jobs.
Regardless of politics, Barbara Bush was beloved because she exuded strength, honesty etc. Eleanor Roosevelt was beloved because she went to bat for people, stood her ground and pushed an agenda.
That is all I have…