I happened to working on a project looking at the impact of certain new technology-based finance plays on bank revenues a little while ago. For the (European) banks that we were looking at, net income for those functions broke down as 24 per cent from transfer functions, 43 per cent from payment functions, 19 percent from pooling functions and 14 percent for the rest. In other words, payments were about the biggest fraction of net income, and this income is under direct threat from alternatives (by which I mean instant payments and such like, not Bitcoin).
According to McKinsey, global payment revenues (which average 40 per cent of bank income worldwide, slightly less than in Europe) are about $1.7 trillion and will reach $2 trillion in 2020.The biggest fraction of this income (around a fifth) comes from the balances on payment accounts (in other words, interest foregone). Hence you can see why banks are worried that if payments shift to non-banks who hold those balances under non-bank licences (with lower regulatory costs attendant) they stand to lose a big chunk of their income.