Actually, you can sort of formalize the argument: Software is eligible for copyright. Therefore, the law already recognizes that it is an expressive activity.
A mechanical device is already not eligible for copyright.
Software is the only thing I know covered by both patents and copyright. Sometimes people deny this to me when I say this online, but I haven't yet heard anybody come up with a concrete example that stood up to scrutiny. Is it really so stunning that two systems never designed to mesh, patents and copyright, turn out to in fact not mesh and produce a big mess? Is it really so horrible that software be only copyrightable and not patentable? Very few people are arguing that software should not be covered by any sort of IP protection, and I suspect the non-zero set of such people would be further shrunk if patents were removed from the equation. (Though I also guarantee, not eliminated.)
Regarding my initial point, I think software falls under copyright solely because its written - I don't know if that's the argument now, but I imagine that was at least the initial reason for granting copyrights. Personally, I can find no meaningful difference between designing software and designing a mechanical device. For that reason, I don't like that argument.
Your main point is interesting, but I'm not sure if I can completely go along with it. Consider, say, a mechanical latch. The design schematics for it fall under copyright. The latch itself falls under patent. The process for making the latch is to look at its design, and change your tools around to produce something of that design. Looking at it this way, I can see how software could be considered its own design schematic - yes, I'm aware that external documentation exists, so it's not a perfect analogy. But with software, there's no separation between "thing used to describe what should happen" and "thing that happens."
I want to agree with your argument because it would provide a clean solution to the problem, but I don't think I can. Rather, I think the solution to the problem may require a results-oriented approach. That is, it may require us (as a society) to say, "The current patent scheme regarding software is harming innovation. We are going to change how patents apply to software to avoid this harm."
"Regarding my initial point, I think software falls under copyright solely because its written"
No. That's a degree of misconception that I can't fix in an HN post. Copyright has little to nothing to do with the medium in which an expression is fixed. And with all due respect, the rest of your post is so muddled w.r.t. what copyrights really are that it's hard to even address what's there. (I truly mean "with all due respect", but I also truly mean that it is very muddled.) You really ought to spend some more time studying the topic, including such basics as what exactly copyrights are and what, exactly, they cover, and why.
What I meant was, "it's fixed somehow". I assume the original reasoning for why code is copyrightable is that when I write, say, a book, that is copyrightable. Code is written down just like a book is, so it follows that copyright will apply. I'm not saying that's the legal reasoning. I'm saying that was probably the initial gut-reaction to why copyright should apply to code, and the legal reasoning came afterwards.
I have spent time with the various forms of IP, and I feel I have a pretty good grasp of what copyright is. I can't correct any misconceptions unless you point them out - although I have a feeling it's more that I did a poor job of expressing myself.
Attempt the second: with non-software inventions, you can have a copyright on the documents that explain how to build the invention. You can have a patent on the invention itself. Software can be both copyrighted and patented. You object to this because it's the only instance we have of something that can be both copyrighted and patented - it's a unique exception. I responded to this objection by pointing out that software is also unique in that what you use to describe exactly how to make the invention is the invention itself.