Yes, revenue provides cash flow, not profit. And costs provide the other part, as was already mentioned. But if it increases cash flow without increasing relative costs, it increases profit. Do you think banks would charge fees if they could make more money by removing them? Again, the banks are largely in control of these costs, like the amount of cash back they provide. For example, the federal reserve reports that bank fees account for 1.82% of purchase volume, while cash back programs account for 1.57% of purchase volume. In other words, they make a profit on balance.

You can read the financial statements to get more information. That's where the above numbers came from. They don't generally say "Fees contribute to X% of profits" but they do indicate they are relatively large parts of revenue. For example, JPMorgan lists $5.97B in fee revenue and rewards cost $4.28B, with the difference being profit. So where are the extra costs you are implying coming from that make fees a net cost?