My good bank (First Direct) has done really well at this. I can call them about anything 24/7, a human answers about as quickly as a person would answer their own phone, maybe 5-10 seconds, not long enough for one of those stupid "We're very busy" messages. But I rarely talk to them because all routine stuff just works correctly so I don't need to. I called them once to ask what happens if I need a whole lot of cash right soon (since they don't have physical locations, the answer was for very large amounts I need to give a lot of notice but a courier brings me the cash) and decades ago I called them because I wanted my debit card to work in the ATMs for other banks (remember when it didn't? Maybe you're too young). Also I called them to transfer money to buy my current home because that's too much money to be authorised by a web form apparently.