> It is vacuously true that a Turing machine can implement human intelligence

The case of simulating all known physics is stronger so I'll consider that.

But still it tells us nothing, as the Turing machine can't be built. It is a kind of tautology wherein computation is taken to "run" the universe via the formalism of quantum mechanics, which is taken to be a complete description of reality, permitting the assumption that brains do intelligence by way of unknown combinations of known factors.

For what it's worth, I think the last point might be right, but the argument is circular.

Here is a better one. We can/do design narrow boundary intelligence into machines. We can see that we are ourselves assemblies of a huge number of tiny machines which we only partially understand. Therefore it seems plausible that computation might be sufficient for biology. But until we better understand life we'll not know.

Whether we can engineer it or whether it must grow, and on what substrates, are also relevant questions.

If it appears we are forced to "go numerically", as you say, it may just indicate that we don't know how to put the pieces together yet. It might mean that a human zygote and its immediate environment is the only thing that can put the pieces together properly given energetic and material constraints. It might also mean we're missing physics, or maybe even philosophy: fundamental notions of what it means to have/be biological intelligence. Intelligence human or otherwise isn't well defined.

QM is a testable hypothesis, so I don't think it's necessarily like an axiomatic assumption here. I'm not sure what you mean by "it tells us nothing, as ... can't be built". It tells us there's no theoretical constraint and only an engineering constraint to doing simulating the human brain (and all the tasks)