The wireless thing is because the phone companies treat the account as a credit account. The easy way around it is some prepaid plan (which is possible to fund in cash...). 5 years ago it wasn't such a good option. These days a $50 prepaid plan is at least reasonable, even if it isn't the best option.
For cellular, prepaid seems to solve all of the problems everywhere I've been. I ordered a prepaid SIM card here in the US over the internet with nothing but a credit card number, has full data service and everything. Same thing everywhere else I've travelled in the last year.
Around the beginning of 2013, I took a trip to UAE, Norway, and the Netherlands. In each of those, I was able to get a prepaid SIM card at the airport for cash, with nothing but a passport for ID. All with phone, text, and data service.
I also knew someone who paid their phone bill in person every month because he was a teenager and didn't have a checking account, but had a cell phone bill.
When I set it up, it required a phone call to turn on, and my name, um, not sure what else. No bank account or anything else. Just a phone call with my name.
First, if you have just move there, and don't have a bank account, you don't have checkbook either (there are countries who has no checks at all) - no check by mail.
No utilities accepted credit or debit card, they always wanted to have a proper bank account number from me. Later on they have improved their system and now they offer online bill pay, with an extra "convenience fee" for credit cards. Hurray! (Although I am not sure if the bank account is still a requirement for opening.)
Btw. similar story applies for wireless service: I was required to provide my full employment contract to receive a simple phone number (at that point I had bank account, active employment...). How weird is that?