Then that would be yet another non-cooking thing that it does. Not evidence that it can't be a good cook. I'm sure somebody out there paints acrylics on cast iron pans

Look, there is a lot of pro-AI nonsense going around right now that I too would like to shut down, but none of that changes the fact that to prove that a machine is incapable of a task requires an experimental structure in which the machine is performing as best as it possibly can and still comes up short, or an argument based on fundamentals about what the machine is (e.g. a steam engine can't move faster than the speed of sound in steam).

No pile of failures, however embarrassing, can prove the impossibility of success, that's just not how evidence works.