One's goose being cooked is an idiom from at least 200 years ago. The transfer of that meaning to generally being a single adjective rather than a full phrase is probably at least 100 years old.
And as more evidence, here's an issue of Boys Life magazine, from August 1938, that uses the phrase "he's cooked" to describe someone who is going to lose a sporting event. So it's at least 87 years old, maybe older.
The "mental illness" and "plumber" categories can actually add up to be more than 100%.