I'm not trying to play burden of proof tennis here but surely the fact that the only "intelligence" that we know of is implemented in a massively parallel way should give you pause as to assuming that it can be done serially. Unless of course the kind of AI that humans create is nothing like the human mind, in which my question is irrelevant.

But that doesn't seem to me to be evidence that such algorithms would be qualitatively different from what we do have.

But we already know that the existing algorithms (in the brain) are qualitatively different from computer programs. I'm not an expert so apologies for any mistakes but the brain is not massively parallel in the way that computers are. A parallel piece of software can funnel a repetitive task into different processors (like the same algorithm for each value of a vector). But parallelism is a built in feature of how the brain works; neurons and clusters of neurons perform computations semi-independently of each other, yet are still coordinated together in a dynamic way. The question is whether algorithms performing similar functions could be implemented serially. Why do you think that they can be?

Regarding computational parity: sure I never said that would be the issue.