The lowest common denominator is NOT "statements" or types of "accounts", or "disclosures", but rather the legal definition of "in writing."
All of the types of consumer products you listed are subject to one or more federal consumer protection regulations (E, DD, Z, etc.) requiring disclosures. While the content and timing will vary (depending on the type of product and the nature of the event triggering the disclosure), many of these assorted disclosures (including the ones printed into your "statements") must be delivered to the consumer in writing.
Pre-2000, that meant paper--only. Now, ESIGN allows electronic documents to become the legal equivalent of paper. In order to obtain ESIGN's license, you provide a series of how-it-works disclosures and obtain the consumer's consent to those terms.
Of particular importance is the how-it-works disclosure required by Section 7001(c)(1)(B)(ii):
(ii) ...whether the consent applies
(I) only to the particular transaction which gave rise to the obligation to provide the record, or
(II) to identified categories of records that may be provided or made available during the course of the parties’ relationship;
In order to accomplish your objective, you would simply need to reword this part of your pre-consent disclosures!
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...gone fishing.