EU has a cap on card fees, and low-income people have no problem opening bank accounts. They do get totally shafted on overdraft fees tho.
Not that you need to fight caps on card fees.
I would hazard a guess that most banks in fact make most of their money through lending your funds to other people.
Could say the rich subsidize the poor in USA (by keeping more in 0.0001% interest checking accounts and more card swipes per month).