[jmbwell]

It provides a way to preliminarily validate the number without having to waste an API call for verification of a malformed number. If it doesn't check out, you can kick it back immediately. I don't know whether this was the intention with credit cards, as those were initially largely used offline and processed in batches, but for lots of numbers with this kind of error checking built-in, offline validation can save a small amount of effort/expense that adds up when you are dealing with a high volume of transactions.

In terms of storage and communication, there's a benefit in being able to verify some degree of data integrity as well.

So I would hazard it's totally a processing thing, not really an identity thing.