Earlier quoted context omitted.
> My bank has made it (almost) impossible to make payments without a phone, btw My bank has several buildings full of people, all within driving distance of my house. Any of those people will happily accept a stack of paper bills. If you don't want to use digital forms of payment, why on earth are you using a bank that doesn't have physical branches located near your home?
Any of those people will happily accept a stack of paper bills. Have you actually tried depositing large amounts of cash on a regular basis? Sounds like a good way to get your account flagged and suspended. Not to mention the Treasury's seeming animosity toward cash as an instrument of payment.
But yes, you can go into banks and deposit money (even frequently, and in reasonably large amounts).
The flagging and suspending stuff is more what I'd be wary of using paypal or something similar, not an actual bank.