I don´t really know how the markets work. Yes, Bannis prefer markets but they don´t walk any distance to use one. How far do people walk to a market to get their food there instead of a closer barn? (or in this case a tavern). There´s a common misunderstanding that people living inside a market circle also use the market as first place for supply but I´m pretty sure that it´s not the case. It´s a happiness circle not more not less and has nothing (or at least nothing directly) to do with the preference to collect food to their houses. People who live close use it even if there´s a barn closer, people at the far end of the circle will primarily use the close barn instead. I made several of these experiments in the vanilla time. But it wasn´t easy to set a distance.
Anyway, I built some more stores in that game closer to the houses that stored a lot of meat from the tavern and the amount of roasted meat in the houses went down. So I don´t think the Bannis see the tavern as equal to the market. Houses close to the lanthandel didn´t contain any/much? roasted meat, also those next to the tavern. But maybe they prefer it over a barn. I don´t know. Could the distance they are willing to walk to a lanthandel be shorter than the distance they are willing to walk to a vanilla market?