I've seen the same policy applied at fast food drive thru windows. (Once, when encountering a fast food restaurant who had closed inside but still served from the drive thru window for another hour, we tried it on foot and bicycle. They refused to serve us. Seemed kinda silly at 11:30PM, with no one around they wouldn't serve us food unless we were inside a car.)
I think that the fast food folks feel it's a safety and security issue for their employees. That's probably the same reason that the inside is closed.
I can't say about banks, especially if they use one of those pneumatic tube systems.