Couldn’t Lightning Network be used to fight spam? Each relay could impose a fee, one too low to be material for ordinary users but high enough to thwart spammers. The fee could increase exponentially with note size, ensuring that we don’t get a repeat of what happened with USENET, with people posting encoded binaries and whatnot.

Or what about some sort of proof of work threshold that must be satisfied prior to a relay accepting a note? This worked well for BitMessage.