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Are humans able to destroy all this habitat because they've got a better brain architecture, because they are able to achieve higher brain mass (because they don't need to fly to survive), or because they have opposable thumbs?

There's too many confounding factors to say that the human brain architecture is actually 'better' based on the outcomes of natural selection. And if we kill all the birds, we will lose the chance to find out as we develop techniques to better compare the trade-offs of the different architectures.