I've had several accounts "cram" me into electronic statements by sneaking some wording in somewhere that if you look at a statement online or something that you are automatically enrolled in electronic statements. American Express did it to me, Best Buy did it to me. Then the problem is that they don't bother to send you statement reminders in email either, so at some point you just start getting calls from them asking why you haven't sent a payment and start racking up huge late fees.
Even if they did send a statement, which they didn't, I checked spam and everything, it is not just the technically clueless who get the shaft, it is the technically competent as well. I get dozens of e-mails a day. If I get an email from a credit card, unless I am at that very moment prepared to deal with it and pay it, it is just going to get put on the back burner and ultimately forgotten. My paper bills sit in a pile on my desk, in date order and get dealt with.
Also, paper statements are not available online forever. If the government comes after you, they can demand paperwork for in some cases 7 years, and in some cases, from the beginning of time. It is up to you to have that information available, and if you depend on your third parties to keep that for you, you are SOL. Basically you need to save a local copy electronically, or print it out and store. So they are outsourcing their cost of doing business to you without providing you a nice discount for performing their job for them.
As far as banks go, I go to my bank about 3 to 4 times per week. Most of those are for deposits. Yes, my bank has a mobile deposit app. Yes, like most banks, they charge a convenience fee for something which is a convenience for them and an inconvenience for you. The tellers are still free, so I make my deposits in person at the bank, where the tellers all know me and personally greet me by name.