Going the other way, it’s not clear that a Turing-complete model of computation can tractably implement (say) crow cognition. Turing machines can solve arbitrary systems of Schrödinger equations, so theoretically we could simulate every atom in a crow’s body and get an AI crow[1]. But that’s obviously intractable for any known physical computer, and would remain intractable even if we moved to proteins rather than atoms. So are there higher-order “primitives” of crow cognition that can be implemented on a Turing machine? Or is the problem akin to integration, where neat “symbolic” solutions are impossible for most brains, and only “numeric” approaches work?
[1] This is also true for humans: even if you take a loopy quantum consciousness approach, AGI is theoretically possible. Sometimes you see people arguing against AGI on the grounds of Gödel-incompleteness, but this is a mystical nonsense understanding of what Gödel actually proved.