The problem stems mostly from the way research funding works, which promotes a competitive stance instead of a collaborative one; scientists try to publish to the highest impact factor journals possible and often hide important details so that other research groups do not publish any new findings before them. On the other hand, I'm not sure what a good solution to this problem would be but I hope someone comes up with one soon.
While this problem may be true of certain poor actors in some fields of science, I would argue that it's far more the exception than the rule.
My experience (in genomics / evolutionary genetics) was overwhelmingly positive, with huge amounts of collaboration all around. Scientists did try to publish at the highest-impact journal because they care about their career prospects, and there were often competitive labs racing to the finish line with a breakthrough publication.
But I never saw researchers withhold important details in order to accelerate their own publication or to hamper the efforts of others. By and large, I saw huge teams collaborating on large projects with a deep sense of purpose to move the field forward and improve understanding.
In fact research funding in genomics became so collaborative — with increasing portions of the research budget being put towards huge consortium-based projects — that smaller labs began criticizing funding agencies because their smaller projects weren't being funded. These projects are typically more competitive and higher risk, yielding potentially high-impact articles with a far smaller number of authors.
What's the answer in the end? As with many things, it's balance. Cooperation is great, but to a fault. Sometimes having small labs working in relative isolation, even competing against other small labs, can yield great innovation and progress. Other times you need a huge collaborative effort to do something big, expensive and important for the future of the field.
I think ego and the patent system take a big part of it. Imagine a country funding research related to cancer. The best outcome will be to cure it. It doesn't matter if you share some of your research and scientists from another country or group solve "the last mile".
The issue in this scenario is how the patent system currently works. Instead of giving the ownership to the scientists who make the breakthrough, the discovery must be shared between the different research groups.
Not sure how important is the role of a patent system here. In theoretical physics and astronomy, despite having no need for patenting, the problem still persists. I would say that the standard university publish-or-perish model seems to be the main obstacle in the road to open research.
Do you remember the name of the third astronaut aboard the Apollo 11, aside from Neil Amstrong and Buzz Aldrin? If no, then you can imagine why for somebody may matter who solves "the last mile". Not saying it's not a problem, just that oversimplifying is probably not the best approach.
