The particular choice -- as the developer of the network, not a client of it! -- is arbitrary, or at least arbitrary within some constrained range. As a very simple example, imagine that one candidate hash algorithm favors hardware produced by a violent, morally repugnant regime and another favors hardware produced by a regime you want to support; why would you -- again, as the developer of the system, not a user of it! -- choose the former over the latter?
I will not succumb to your
reductio ad absurdium argument, but rather I will point out that, when you are designing a system, you tend to focus on just the system and the immediate problem. Yes, the design choices are arbitrary, but the job of the designer is, by definition, to make arbitrary choices. Satoshi was designing a digital currency system - why on earth would he include something totally unrelated to digital currency?
I'm not certain what the argument against trying to find a more productive side-effect for the mining process would be. The difficulty of the task need not be narrowly predictable for a protocol similar to Bitcoin to work; it just needs to be predictable enough.
Well, I'm going to go out on a limb here and potentially alienate myself from a lot of the people who've been around longer than I have, but there seems to be almost a reverence for "the way Satoshi set it up." It seems that Satoshi and an anointed few have the master plan for details of the road map, and any deviation from that is frowned upon.
Now, putting aside my cynicism, I've already outlined a potential argument against different proofs of work, namely that you need a problem that can be easily verified and cannot be cheated. I don't know if those problems can be easily verified. The amount of work required to modify the system to allow different types of proofs of work is probably far more than the benefits Bitcoiners would derive, especially for something that's considered a "nice to have."
Some more potential arguments:
What if someone doesn't agree with the project that's chosen as the beneficiary of the work? Can we find a project that everyone can agree on? What if we don't? Do we deny someone access to Bitcoin because they don't agree with the beneficiary? That doesn't seem right to me. Your same
reductio ad absurdium argument can be inserted here with little modification.
Bitcoin is open source, and anyone can review the software. At the moment, it requires a basic understanding of cryptography to verify that the code does what it claims to do. If you add in protein folding, then in order to understand and verify that the proof of work cannot be cheated, then you now need to become familiar with protein folding. If it gets changed to finding more values of pi, then you have to become familiar with how to calculate pi. The more problem domains you add, the more complex the system becomes, and the easier it will be for someone to exploit a weakness and cheat.
I think that's the most compelling argument: it adds unnecessary complexity. As an expert on cryptography, and by inference an expert on security (the two are not the same), you know that complexity is the antithesis of security. The existing system is simple, it works, and is secure. Yes, it would be
nice if it did something that also had a useful side benefit, but I will take simple and secure over complex and unknown any day.