Not really. Rural America you don't need a mobile phone. I can go days without ever touching my phone. And if it wasn't for my bank, I wouldn't need it at all. Even then I could just go to the bank but I'm too lazy to do that.
Even in NYC you could get by pretty much just fine without a phone (a credit or debit card is pretty much required though). The hardest part would be losing contact since expectations of how people organize and meet up are completely mobile phone centric, and plans are almost expected to be modified in real time.
The "I can't bank" complaint is strange to me. I've never done any banking on my phone, the closest is when paypal extorted a phone number out of me for SMS verification. I still do banking through web browser at home, for several different accounts. But maybe it's different outside of the US.