How dos the cop role give out information they received without the Mafia tar-getting them? Wouldn't the cop store the information, hoping to build up the list and skip the lynch until they have gathered enough names? I think after the cop comes out the 1st time, it'd be a huge red target on their back.
This isn't really relevant to any of the discussions, just curious as I've thought about this and my only other idea is a protection role protecting the cop for another night, but that would require the protection role actually helping and who knows how long that'll last?