> What are the branches even for if not customer support?

Lots of physical locations make the bank seem big/safe/reputable.

Beyond that, it's sales and a place to have ATMs. I have sometimes been able to get a replacement card issued at a branch instead of waiting for one to show up in the mail.

Some branches will accommodate special requests like "can I withdraw $200... in two dollar bills" / take coin deposits but that's been increasingly rare.

My local branch has had a sign on the front door "our coin counter is broken, sorry for the inconvenience" for the past 6 months. I refuse to believe they don't have a working coin counter in a bank branch; they just don't want customers bringing in a big jars of coins.