Don't forget that many (perhaps most) online banking systems do not provide the on-statement disclosures that are required by Reg. DD, and omit much of the information required by Reg. E.
You simply cannot stop the paper statements unless you can provide all of the required information appearing on the paper statement in an electronic format, and get the customer's demonstrable consent under E-SIGN.
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"I guess I should warn you, if I turn out to be particularly clear, you've probably misunderstood what I've said." -- Alan Greenspan