It's not a big deal, because you usually arrive at the baggage claim long before your bags do.
Some airports have employees that match claim check with bags in order to prevent theft and accidentally picking up the wrong bag.
What's idiotic is that they usually leave once everyone has picked up their bags. That means a thief can walk in, pick up whatever bags are still unclaimed, and take them home.
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"It's as easy as 1, 2, C" -- Kelly, Married With Children