Rabbi,
Entirely on-line isn't really correct. They have something like 4 offices in the United States.
Which means that for all intents and purposes they are an on-line-only banking institution for the vast majority of the people who use them.
I'm not going to drive to Wilmington, Philly, NYC, or LA to deposit a check or get $20 on my way to a gunshow.
It's true that many (if not most) financial institutions are now so "wired up" that they can be virtually on-line-only for many people. Navy Federal, my primary financial institution, is certainly that way, and I do the majority of my financial business with NFCU online, but if I need to, from work or home I can be at an NFCU office or ATM (any of a number in this area) in a matter of minutes.
I've gotten a LOT more used to the on-line banking concept over the past few years. Working at NFCU and writing a lot of the marketing materials that were used to educate our members certainly helped, but I still like the ability to hit the brick & mortar if I need to.