You can though. Precisely because there are countries (past and present) that have / had no legal framework for such incentives, and there are others where the framework was there but the law is not enforced. And we can observe how it is working for them, compare and contrast. I live in one of them (lived here all my life) but work for countries that provide such a protection (precisely because my intellectual property would not be respected here, so my own country my homeland does not get to benefit from my work) so it is easy for me to look at both sides of the coin - though it is not strictly necessary. It doesn't take hands on experience to observe that the most productive and innovative countries occupying planet earth are those that have strong intellectual property rights.
There is a lot of low hanging fruit where I live that would double the GDP of the country in a few years but no one is doing it, because they are either capital intensive, or time intensive (or both) but without any protections there to make it worth your while it doesn't make sense to attempt those - for anyone. It makes more sense to pitch any innovative ideas to countries that will protect you so that you get a return proportional to the value you generate for the rest of the society. If I have an idea that has the potential to shave 1 hour off of millions of people's work everyday, that is enormous value generated for everyone and I should be rewarded proportionally. Not to mention the risk I'd have to take to attempt that, by attempting that I'm doing this instead of doing something else with my only life so of course the incentive HAS TO be there.
>The think tank researching a cure for cancer will still have ample funding sources from those who think not having cancer would be beneficial regardless of those sponsors ability to profit off said cure.
I think this is far too naive way of looking at it. You are taking risk entirely out of the equation. If I'm attempting to do something that is of value to other people, merely by attempting it, I am taking a RISK. My time is my most valuable asset, I only live once, and I'm willing to invest my time and capital into this endeavor instead of doing something else with them. The resources of human beings are not unlimited, so they need to have a heuristic / algorithm to ration their resources. Their survival / wellbeing is dependent on this. So something becomes a viable risk only if there is a possible return that makes sense. Like you wouldn't play coin flip for 1.1x or nothing right? It must at the very least be 2x or nothing to break even.
So we think we'd like to do good for no possibility of personal return, but behavioral economics show that humans do not operate that way (even though they'd like to think that they would) because each and every human being have their own lives, responsibilities, families, wants, wishes and only limited resources. To make ANYTHING the returns must be congruent with your heuristic about how you'd like to divide your limited resources.