Like any baggage tag, these provide ID in the case of loss. Whether it is lost through AC or another airline's misdirection, or another reason, by delivering it AC it is assumed you can be traced by them since they have your contact details on file. It is more secure than having your full address and other information displayed on a business card or other form of tag.
But it is also a status thing, which may not matter to some, but does to many others. Just pay a visit to any US airline lounge, or on a flight, and see how often these things get "exposed". Why do some people have platinum credit cards, others stick with gold, and still others who could have either, remain with basic ones?