Upon a slight re-read, it seems that SDF's have a lot in common with magnetism, and potentially gravity? (ie: what is the closest "reacting" force)
Your visual examples made things pretty clear, and I appreciated the simplicity (it's just "what's closest"), and humility (all that work to end up 'worse off').
I will check it at home, I have started my PhD recently and I find the subject very interesting. It got my attention after reading some papers (i.e. DeepSDF). One of the best pages on the subject is Iñigo Quilez's blog: https://www.iquilezles.org/index.html
"A lightweight signed distance field editor and renderer" sounds like such fun to play with. Manipulate implicit surfaces by hand. Or script. Perhaps using keyframes. And output deformable 3D morphing mesh animations ;)
…very decent blog post!