Based on your definitions, would you agree that real diversity is immeasurable, and that the only way to foster real diversity is to allow "fake" diversity to thrive?

Viewing diversity as a means to an end, which is productivity, will never work without a wider context. Humans are ends to themselves, and trying to optimize for "productive" diversity will always backfire. Diversity leads to both beauty and ugliness, productivity and stagnation, [thing-you-like] and [thing-you-don't-like] - you can't have one without the other.