My guess is that custom proteins are harder to synthesize on demand. Generally if you want a custom protein you synthesize the DNA coding it, then insert it into a cell and have it produce the protein. Plus, DNA can be duplicated in vitro through conventional PCR where it's not really viable to transcribe proteins outside of a living cell.

... that's better

Alas, there is now 1+ Ringworld Reference

Of course the brain is turing complete. You can prove it the same way you prove any other machine is turing complete: it has the ability to simulate a turing machine. I can simulate a tape driven turing machine pretty damn easily with a sheet of paper and a pencil. I think you're confused as to what "turing-complete" means. Solving the halting problem is not a requirement. In fact, you can prove that a turing machine cannot solve the halting problem. So the brain's inability to do so doesn't have any bearing on whether it's turing complete.