I do agree that it's B.S. to say that legal challenges prevent investment in cancer research (unless people mean "coconut oil cures cancer" type of research, in which case they well should). I would probably say that if anything current patent law makes cancer research more profitable that it would be without it (however, I don't have enough of legal background to speak definitively on this).
The question for me is why is this true? It seems like there should be.
I imagine power law holds in most disciplines: going from 99.99% uptime to 99.999% is far harder than going from 99.9 to 99.99% which in turn is harder then going from 99% to 99.9%. Likewise, I'd imagine same holds true with death tolls over N years from various illnesses (but obviously with different constants involved).
Can you explain to me what you meant by externalities here? Do you mean medical industry benefits from cures without contributing to funding the NIH grants?
I wonder if an X-Prize like model might work better here, with, e.g., individuals with genetic risk for a specific cancer "crowd funding" various grades of prizes, with the actual awarding of prizes, setting and advertising the prizes, being done by an organization/consortium that knows what they're doing.
As someone else noted, "saving the world" usually translates into economics as "generating large positive externalities". It's not just that you might have to give out cancer cures for free (in most countries the state will pay for health-care anyway), it's that you simply can't patent the Theory of General Relativity or the Germ Theory of Disease or the Dead Germ Method of Vaccination. Even improvements in nutrition and yield of crops can only partially be treated as private, excludable property.
Radical new discoveries are almost always nonexcludable, and thus can't really be treated as private commodities sold on a market. Note that I said can't, not shouldn't: trying to treat nonexcludable goods as private commodities leads to bankruptcy rather than sin.