My remark about 'Kelly' is tongue in cheek; I think Fuld was bending over backward to put Kelly on an equal footing in his little write-up.
I want to re-read what Handy said about it.

The theme is old; "To sigh yet feel no pain... and ending up with

To think all other charms divine,
But those we have just won;
This is love, careless love
Such as kindleth hearts that rove."
See thread 81179, where I quoted part of this song from Thomas Moore, c. 1800, and which was in 19th c. American sheet music. Is it a precursor?? Dunno.

81179: Moore song posted
50989: Kelly's Love posted
58163: Careless Love 1925
(Bessie Smith)
58247: Careless Love various


I have not found "Loveless Love" by Handy; only versions by singers claiming to have his lyrics.