What's the difference between, say, M&T, and an internet bank? You may not be able to mail checks to M&T, maybe you can, I don't know. But you can also log on to M&T and do all your banking online. Checks are a thing of the past anyways. Most people do EFT. They get direct deposit. If you want to use technology to make check deposits, you can always use an ATM. I don't think M&T or banks in general are going to be wiped out by internet banking. They have all the features of internet banking plus local presence. What happens when you want to withdraw money out of an ATM? What happens when you want to take out a loan and talk to a loan officer? What if you want to get a notary? What if you want to put something in a safe deposit box? These are all things internet banking won't let you do. What if you have a large CASH deposit, are you going to send CASH through the mail or go through the hassle and expense of turning it into a cashier's check to mail it? No thanks, no internet banking for me. Sure, I have a brokerage account but I don't use it for banking.
I am not a customer but I am a shareholder. If it really disturbs you that you have to use tellers, use ATMs or maybe look into seeing if you can mail M&T a check. Then if you want to do something in person, you have that option, something you will never get with one of these internet banks.