Intuitively, I agree with you that software patents are a bad idea, but patents are supposed to be available for both devices and processes (along with plants and some other more complicated things).
An algorithm is a process, and while it's clear that just doing something on a computer shouldn't be patent-able; I think there's a case for granting patents to innovative and useful algorithms.
Patents actually are not supposed to be available for processes! That was something invented by the courts (in 1998: State Street Bank & Trust Co. v. Signature Financial Group). Congress has passed no legislation regarding process/business method patents and software patents are a further extension of business method patents.
The core of the problem is method patents to begin with. I think everyone here pretty much agrees at this point that software patents shouldn't exist but really, why should any process/method patent exist?
Most of the arguments against software patents also apply to business method patents. I say do away with both.
It's better to err on the side of not granting them, than on the side of what we have now with sickening patent trolling and patent protection racket slowing down progress.
An algorithm is a process, and while it's clear that just doing something on a computer shouldn't be patent-able; I think there's a case for granting patents to innovative and useful algorithms.