Trivial solution: I walk to bank some day once a month, give them cash, give them account numbers, sent. It'd be done in all of ten minutes.
Does it exist where you live? Maybe, maybe not. Hell, if I knew you I'd do it for you, I'd enjoy obfuscating my accounts.
And no-one is saying that literally every transaction has to be done in cash, just that it should be _possible_ to do so.
The idea that cash is this hilariously inconvenient thing is a complete fabrication and I frankly tire of that discussion. You're talking about moving small physical things, it's a solved problem, everything around you right now is a small physical thing.
edit: posters are responding about the businesses that exist in their area. by this token it's "inconvenient" for me to use cash because the japanese place down the road doesn't take it. well no, they're just being dicks, there's no _fundamental_ inconvenience.