Perhaps it would be more accurate to say: If people didn't have to do work that gets paid, then they wouldn't do the work that society needs/wants them to do. To the degree that markets work, money incentivizes people to do work that society feels is important.

A farmer might still plant, but decide to plant flowers instead of food. Or maybe they would plant exotic fruits instead of staple foods.

A programmer might still program, but they might decide to play with algorithm problems instead of developing medical software.