Here is a bit more gasoline for the fire.
My wife has had a generic low shank ZZ walking foot in her Bernina case for years. It came with a metal Bernina to LS adapter. Last year I took it out and put it on several of our LS ZZ and straight stitch machines and it worked. The walking foot feet does not match the feed dogs of the straight stitch machines, that is true, but it does work. I've used it. I posted pictures of that ZZ walking foot mounted to my Singer 66 Treadle #2 quilting it's cover.
OK, late last year I bought one of Sew-Classics straight stitch walking feet. I tried it on many of our machines and it would not work. I don't know why. It looked good, fit, functioned, but would not work. In each case I put the generic LS ZZ foot back on and it did work.
I got a credit for the WF from S-C and have continued to use the LS ZZ foot.
It's my experience that just because the feet don't match doesn't mean it won't work. I think there is more to it.
I'm hoping that somewhere there is a Singer made LS SS WF and when I find one I'll buy it. Until then I'll stick with the generic LS ZZ WF.
Just my experiences.
Joe