It's sometimes done, though uncommon. But the bag claim check is just like any other claim check.

You have to present a claim check when you pick up your dry cleaning, your valet parked car, or your coat at a theater/museum coat check. In each of these cases, you entrust your belongings to a third party, who then requires you to produce the claim check to get them back. I don't see how this is different. It is definitely NOT the same as having your belongings or your person searched or being questioned.