1) Float. Every dollar that is held in limbo 'for checking' is interest income to the bank.
2) Rabid identification requirements lower the risk of new account fraud (which is paid by the bank).
3) Information on who you're sending payments to is usable by the bank for prospecting and risk analysis.
4) If you read anything about regulatory capture, it explains how regulation is used by incumbents to discourage competition. i.e. No new banks have opened in the U.S. since 2009, when new regulations to prevent banks from getting bigger were passed. <- And now, the biggest banks are MUCH larger.
From 2009 to 2013 only 7 new banks were formed, fewer than 2 per year.
Many industry observers have suggested that the decline is primarily due to regulatory burden, including new FDIC regulations and the 2010 Dodd‐Frank Act. But other influences could have played a role, in particular, the current weak economy.