Would people rather be required to wait in line to show their baggage claim check to an employee before leaving the baggage claim area on every flight, or would you rather accept the infinitesimally small risk of baggage theft (which the airline will compensate you for in cash anyway)?

Also, if you don't have your baggage claim check for any reason, you could be required to show a boarding pass with confirmation number, or be redirected to the baggage service office for verification. Sounds like a lot of work with little benefit.