McKinsey is saying the opposite of what you want to imply:

Current accounts are the cornerstone of the European payments business.

Consumer deposits are part of the payments and clearing system, as JakeS has pointed out.

They provide a stable and inexpensive source of funding for banks,

They're talking about current account, not savings accounts or time deposits. Current accounts don't generally pay interest, therefore they are a cheap source of liquidity ("funding" - see also JakeS's comments) in the amount of their average balance. In the US, checking accounts generally have quite stiff maintenance fees unless minimum balances are maintained. But savings accounts or time deposits pay higher interests and are therefore more expensive. Also, some banks aggressively advertise demand deposits (current accounts) paying high interest rates. Those are an expensive source of funding.

and interest on balances provides the major portion of payments-related income in Europe.

If that's bank income, it must refer to interest charged on negative balances.

As banks' stickiest product, current accounts are an excellent basis for selling other products and building a broad relationship with a customer.

Also mentioned in mine and others' comments

Important challenges loom, however. Even as overall payments revenue is projected to grow from 30 to 35 percent of total banking revenues in Europe between 2007 and 2012, income from current accounts is under attack.

This [bank] income from current accounts must be from charges and fees.

There are three stories about the euro crisis: the Republican story, the German story, and the truth. -- Paul Krugman