We most certainly do have this. I have had accounts with 4 different major banks here, and I have never once paid a fee for my checking or savings accounts, except to order checks. Most banks do offer free checking and savings accounts, where having the account incurs no fees. Sometimes to avoid a monthly account maintenance fee you need to meet a minimum balance, or have direct deposit, or use online bill pay. Santander even has an account that pays you $20/month for doing those things.
Fees come about in other ways. When you use an ATM not branded as your bank's, both the ATM owner and your bank may charge a fee, sometimes several dollars each (some credit unions reimburse you for such fees up to some limit, but not most). If you overdraw your account with a debit card, banks will process the transaction but charge a large fee (tens of dollars) for the "convenience" of not being denied (this is supposed to be an opt-in feature now, but they use all sorts of slimy tactics to get people to opt-in). It used to be (iirc this is no longer legal) that overdrafts were determined at the end of a day, but that transactions were processed out of order: all debits before all credits, largest items first, which maximized the number of times an overdraft fee got charged.
So yeah. If you have enough money and/or know your account balance, you'll never get charged a fee and can get your bank to pay you. If you're poor or careless, you get charged for a whole bunch of things.