Yes, that makes sense--one sort of feels that the Shire really has quite a lot of government, it's just disguised as family politics.

Maybe Michel Delving got to be designated such an important site, because it was outside the area of immediate influence of both the Tooks and Brandybucks--a neutral meeting-place perhaps, at a time when there was more potential tension between the Great Families. The office and role of the Mayor suggests to me that that might be the case.