Like Brian, every bank I know gives a copy of the signature card as part of the account opening documentation.
It is the only document provided to the customer that informs them of their agreed upon account ownership designation (multiple party with right of survivorship or not, or POD, etc.), as well as their TIN backup withholding certification.
In short, I see it as an extension of their contractual terms and agreement, and wouldn't dream of not providing the copy. Same with the business resolution.
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Me, Type A? Maybe - I'm not done analyzing it yet.