You don't have to give them a copy unless you intend to enforce the terms against them some day. If your bank is willing to give up the legal protections a contract affords, there is simply no reason to have the customer sign anything.
A bank's signature card is a good example of an "adhesion" contract; i.e. it's presented to the customer on a "take it or leave it" basis. The bank has all the bargaining power and the customer has none. Courts construe adhesion contracts very narrowly against the draftsman; i.e. if it's worded poorly the court will interpret it in favor of the customer.
On the other hand, if the customer gets on the stand and says, "Your honor, I don't have a clue what it says. They never gave me a copy" and your bank cannot refute that, the court will not consider the wording in the contract at all. It will just make its decision based on "what's right."
There is a really good reason why vendors produced signature cards as multi-part forms several years ago and why today's platform systems automatically spit out two copies.
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In this world you must be oh so smart or oh so pleasant. Well, for years I was smart. I recommend pleasant.