I think I see your point. I'll restate it the other way around, though, because that direction makes more sense to me. Please tell me if I got it wrong.
Suppose I have an algorithm for doing some useful transformation on an input. Suppose we were in an environment in which this algorithm could not be patented. I could instead sit on the algorithm and build a circuit in hardware accordingly, patent the circuit, and sell that while keeping the algorithm secret. Ignore that it could be reverse-engineered.
Is that scenario good for anyone? Probably not. It would be better for everyone if the algorithm were made public, even if it were simply unused for the patent term, than if it were to lie hidden on a disk somewhere. Why does it make sense to grant a patent to the circuit, but not the algorithm?
I admit, that situation is a little inconsistent. This is partly because the whole concept of the patent is inconsistent, but we keep it around because we haven't found a consistent way to fulfill the same purpose. Consider a third option, though:
Suppose that the guy with the useful algorithm is Joseph Fourier. He patents the software techniques to produce Fourier series. Now, anyone making software that relies on Fourier series needs to pay Joseph Fourier, which is fine. Anyone who builds a hard circuit would likewise need to pay for the privilege, due to another patent. What about a person executing the exact same software instructions by hand?
Clearly the person may execute the algorithm by hand without paying. Why should they not need to pay, when the only thing the software author has done is the convenient shortcut of using a computer? In order to be similarly consistent, we'd need to require the manual executor to pay. Unfortunately, the manual executor is every collegiate-level math student.