It depends on if you're talking about brokerage or retail branches. Brokerage branches exist for the one guy who comes in and makes a bunch of large investments or reorganizes his portfolio. Yes, this can be done online, and probably more cheaply, but those of a "certain" generation are more comfortable working with another person on the other side of the desk when it comes to their money.

Retail banking, on the other hand, I totally agree with you. Basically everything that can be done in a branch can be done on your phone, faster. And the stuff that can't be done on the app can be done by calling in, which still takes a fraction of the time of going to the branch. I've personally had great experience with bank customer service, and routinely have 5 minute calls with them, whether it's to authorize a charge on my card or change my ATM limit.

Banks definitely see this change coming. It's just a question of when they draw the line between catering to the subset of their customers who prefer in-person interaction and the cost of running a branch (especially when compared to the kind of overhead that comes with running an app).

I'm more curious to see how ATM's evolve.