Chemistry causes another, specific problem: I was told that in the pharmaceutical industry, one would patent one molecule at a time. If someone else found a slightly different molecule with the same effect, the patent offers no protection. It may sometimes forces laboratories to waste their time searching for similar molecules so they can patent them all (or at least a good deal).

So, while such patents wouldn't be bad, the system is still suboptimal (depending on the time needed to search for the similar molecules).

Plus, even if in this particular domain a patent system is better than nothing, it may be difficult to discriminate the domain. For instance, software patents don't apply in Europe. But if you care enough to specify that the whole shenanigan takes place on some sort of processing device, then you can sometimes pretend it is not a software patent. GPS devices for instance are subject to patents, though it is quite obvious that the core of the idea lies in the program, not in the general purpose ARM chip (I don't know about the GPS receiver). But if you turn the GPS device into a general purpose computer that happen to have a GPS program, you may be safe.

I'm not a lawyer, but it looks like any partial ban of patents is bound to be a headache.