The idea is to prove that the issuance of the card was solicited - see 12 CFR 205.5. While the regulation allows this to happen with an "oral" request, most banks from an internal control standpoint, require signed applications. This prevents an unscrupulous employee from perpetuating debit card fraud by issuing cards to customers and then having them mailed to themselves, receiving incentive pay for selling debit cards, etc. It also creates a paper trail for audit purposes.
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