I get that his surname carries certain story with it but zero weight, unless the gramps hid billions of dollars and many companies that the MC will inherit, how can the MC be allowed to vote for anything?
well think it off a tradition/law to prevent family's fighting over seats , 1 seat per family name , family name's tend to stay on the male family side and the settings seems to follow the setup
so if the MC is willing to step up and take the title and vote he can simply because he is off the fletcher bloodline and carries the name, (the feltchers history is also the reason for mr.takumura's rivalry ) so the time already has weight and value , maybe less among the founding family's
the regular people like the baker and such seem more willing and open to help ,which surprised the mc who got good deals from local suppliers
having the mc take a wive off a other family and bearing him childeren will also provide a road to influence the next head,heir to the 5th vote being a grandfather/uncle
so his name and bloodline already have value
the cafe he got and training he had whit his grandfather in a other restaurant/cafe already shows his family is by no means poor
but not all power/influence are based on money or material things , people honor and traditions play a big role to
we get a bit off insight on how the system kinda works
anyone in the founding family's has the right to start a vote/proposal ,but only the family head has a vote ,so 5 votes split between 5 family's
even powerless and/or a puppet for a other family,simply having it be impossible to have draw 2-2 votes will the system function better (or worse depending on votes of course) so they want him in
but to get the 5th and deciding vote on matters they need to convince,bribe and deal whit the MC which will result him in gaining said power,influence or even money
simply put the name and bloodine means power and influence and there isn't a lot you can do about its like being being born male/female you just are