Kristle Cortés of Cleveland Fed has a short note on the topic.
She says though it is true that role of branches in world of mobile banking has dimmed somewhat, but the branches remain important for local information. So the role of branch is likely to shift from being the one that collects deposits/gives credit to the one that collects and maintains information. The info bit role the branch was doing anyways but it becomes more important now:
My study shows that local lenders reduced their lending in areas where house prices were potentially above what would be acceptable based on fundamentals. They originated fewer loans in areas where prices eventually fell, and sold many of the loans they did originate in those areas. These results show that banks behaved differently during the run-up to the financial crisis when they had a bank branch in the area where the property was located.
These findings show that bank branches allow financial institutions access to better information about the local economy, which in turns allows them to make better lending decisions. In general, conditions of the local economy are public information, but as banks weigh the costs and benefits of maintaining a branch network, it is important that they recognize the need to invest in obtaining the type of information available to them when they have a physical presence in the market.
It is important to understand the role of a bank’s branching network as the banking industry introduces new technology that could potentially replace bank branches. As my findings show, even the largest banks can benefit from soft information in areas where they have branches and do in fact behave differently when they have a branch in a market.