An "e-statement" is, at a minimum, two things: a statement of account and required federal disclosures (Regs E, DD, and/or Z).
Unless your account agreements or state law specify any particular content or format for a garden variety statement of account (extremely unlikely), you're on your own. Turning to the disclosures, you need to consider any requirements such as terminology, conspicuousness, boldness, type size, proximity of key items, boxes, etc., etc., etc.
Under Fed regs which have been canceled, you were required to monitor bounce-backs and make additional efforts to deliver the required disclosures. If your e-delivery system was implemented during the years when this stupid requirement was in place, your account agreements and ESIGN opt-in documents may call for bounce-backs to be mailed. If you have saddled yourself with this burden by contract, then that's what you must do. Otherwise, it's your call.
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...gone fishing.