I am in the fraud and forgery field and in my opinion, one reason is if a person is able to steal a check and pass it at a business, if a clerk asks, he may simply write the drivers license number and date of birth of the person he stole the check from, if known. If that happens, then police investigation could turn up a photo, but no personal data of the person with the stolen check. If a thumbprint was used, police would have a thumbprint to match with the photo of the suspect, making apprehension much easier.
I've also found that in counterfeit card cases, specfically, the suspect may have a fake ID to match the name on the card. I figure that could be the case also if someone has written stolen, forged checks. I hope that helps.
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