Franconia has a distinct culture and dialect, so why are similar groups like the Hessians and Thuringians represented by federal states while Franconia is part of other states?
Well, historically, it became part of the Bavarian principality in the early 19th century. Afterwards, the federal states kept their existing borders during the Kaiserreich from 1870. During Weimar Republic, plan were made to restructure state borders to achieve equal land mass in all states. Bavaria already was the right size so it stayed as it was. The Nazis did nor care much for federal states anyway. After the war, the US had occupied almost all of Bavaria anyway so it was again decided to keep the existing borders for the federal state. After the occupation, there never has been a movement to make Franconia an independent state.