I don't think they are unenforceable in general, but they are not automatically enforceable, either. The courts generally apply tests such as "reasonable communicativeness" and the "released valuation doctrine" in deciding whether they are enforceable in the specific circumstances of that case. These tests place burdens and expectations on both parties. For instance, if a passenger's claim for a few hundred dollars worth of jewelry is denied because the CoC excludes jewelry, the courts will likely determine that the passenger had little incentive to explore the limitations and so the burden is higher on the airline to communicate those limitations. But if someone files a claim for tens of thousands of dollars worth of jewelry, then the court may determine that the passenger had a strong incentive to determine the airlines limits of liability and failed to do so.Are you speaking of this specific case? I don't know enough about it to comment either way. My guess is that a suit against the customer would be successful in some jurisdiction.
In general? What's the point of a COC (which all airlines have) if they are not enforceable?
