No. If you follow your agreement, it costs basically nothing. It's true for every mutual transaction (not only for banks). Also no-one forcing you to create accounts in ONE particular bank, you can shop around. there are plenty of options with minimal to no fees accounts.
Other people are going to suggest online banks, which are excellent, but you can't deposit/withdraw cash easily to those, which is the main purpose poorer people have for a bank account.
Instead, try local credit unions. As an example where I'm at, Indiana Members Credit Union has a checking account with all the normal perks of a checking account and no fees. And credit unions work together with the major banks to give their members access at most ATMs.
I wasn't going to, I suggested below. Also it's capital one.
In any capital one branch you can make a deposit/withdrawal with your 360-checking account. If they give you freedom of online-banking it doesn't mean their branches magically become unaccessible to you.
I didn't intend to put down your suggestion, like I said, online banks are great, but there isn't a capitol one, ally, or discover bank in my state. So for people who use cash, a credit union is an excellent choice.
Ironically, people who are being “discriminated” against with progressive, cashless initiatives, live in states where capital one branches and ATMs are on every corner.