> Today banks uses fee for everything and everyone is ok with that

They actually don't. Most ATM fees and inter-bank payments (at least in the UK / Europe) are swallowed by the banks rather than exposed to customers.

> So yes, it is very possible to make a profit by not only having those things but having that without fees.

How? As far as I can tell you're describing a bank that runs deposit accounts but doesn't loan the money back - that is not obviously a profitable enterprise. Something in the whole scheme has to make some money to pay for the employees, the infrastructure, and all the other fixed costs.