Publicly sharing a private key is not equivalent to burning a private key.
It's congruent though.
Discussion
As are these nuts
If a private key is shared publicly then no one can ever be sure who actually signed any particular message. Unless there are IP logs i guess. It's an interesting concept.
A registry of known burnt nsecs (OK OK, publicly shared) with the note ID could be a good thing. If I ever burn this one, I don't want someone then impostering me and people not noticing the note where it was burnt