Basically, the logic behind knowing who Mayor is early is just so that we don't lose information. Even if the chains for each role can only tell us so much, the knowledge that only one pair of people next to each other can be scum could be important information. Basically, for role passing, if two people have a role passed directly between them twice at any point, both of them are fully clear from being scum. Technically we have to contend with scum possibly messing with that information, but it's some nice information to have.
I'm starting to think that maybe claiming mayor the day you have it isn't a great idea 100% of the time. In the case that the player who has mayor has another role, being forced to claim mayor does either one of two things. It either forces them to use the mayor ability (when most of the time they'd probably rather use their other ability), or it tells the mafia that they likely have another role and they should kill them that night. If they have tracker technically Doc can save them, but that's a coin flip in an already unlikely scenario. I think with the knowledge that the people who passed the abilities will know who they passed to we'll probably have most of the information (assuming people actually come forward).
Unlike some of the other people, I was never fully sold on the idea of voting you as mafia 100%, but it's the information we have for now. For now I think it's still the safest play for us, but I'm less confident. Your reasoning makes enough sense for me and it lines up with the stuff we heard earlier. I'd need a veteran player or two to do a soul read to be honest, but it sounds genuine. That's my read, but we have time to discuss more.