Hmmm.
Resisting gravity with an equal force up is not work? None of the four arrows in the classic "image" is actually straight. They are all curved, this is true regardless the genesis of the diagram. In any dynamic system, there is no "fixed" image such that the forces are all "equal". Each vector is a curve, though the motive is to portray a "snapshot". I'm disappointed the "theoretical is eliminated" in the classic portrayal of the four horsemen.
That there is no "movement" means there is no "work"? Hold your fist at arm's length for twenty minutes and say there is no effort (work) involved.
If it helps, consider walking, which is technically simply falling and catching one's fall.
A hover is only slightly challenging, but is perhaps easier to envision.
just a little devil's advocacy, as it were.