> 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.