I appreciate the argument, but it seems like it would invalidate pretty much every patent.
I would be happy with that result, but I don't think that's the case. The problem with the circuit in the example is that it's really just an abstract formula which happens to be represented in the form of a circuit diagram involving ideal components, and the reduction to a physical chip does not involve anything innovative. (If anything, circuit diagrams are even more obviously math than software is. Any circuit diagram is isomorphic to a system of equations.)
Simply designing or simulating something on a computer would not render it unpatentable. Having nothing innovative to offer beyond the abstract design or simulation would. In essence, I'm saying that the natural laws—including mathematics, and by extension software and abstract circuit designs and anything else equivalent to math—have to be taken as a given when considering obviousness. To be patentable, an invention has to offer something more than just the plain natural laws, such as a particular configuration of matter or a physical process for producing it.
Taking software and running it on a computer is always obvious. Taking an abstract circuit design and implementing it with standard circuit elements is always obvious. A previously unknown configuration of matter which acts as a more efficient transistor may be non-obvious. A new manufacturing process to produce a specific alloy or drug may be non-obvious.