I'd argue that the "problem" is that the entire idea that ownership, even temporary, can be claimed on a pre-existing string of bits (and not just some particular method of extracting or using that information) that exists inside all of our bodies, is downright offensive. Moreso because the techniques to isolate and exploit these bit strings have now become commonplace and all but trivial.

And, unlike software patents, they are more likely to represent a significant R&D investment by the applicant.

But the patent system is not a subsidy for R&D costs, it's supposed to protect innovative inventions. I'm appalled at the idea that a research group might be prevented from researching novel therapies that target a particular gene just because some other company happened to successfully isolate it using standard techniques ten years ago.