If publishing which mints you trust is not a privacy concern, then the burden of moving to a trusted mint could be placed on the nutter's client to join the mint, move the funds in, and nut from there.
Discussion
Yes but again moving mint to mint is a lightning hop. Already possible. Pablo is trying to remove the hop. His idea isn't replacing anything, he states in the demo that it is an additional option. Don't trust it don't us it.
If nutter and nuttee are using the same mint then no lightning transaction necessary. Matching up mints could be an efficiency gain. I still don't know whether publishing them is a good idea though.
Privacy of the nuttee is an interesting consideration. Though revealing that information is useful for a web of trust for mints.
Having the nutter pre-swap makes sense, though you shouldn't look a gifted horse in the mouth.