Not unsolvable - just difficult. Systematic problems driven by social incentives are very difficult to solve. But they can be solved. Especially if the institutions in question get behind solving them.

In the case of science, a lot of the bad incentives are created by a combination of the institutions (university administrations and granting agencies) and by the scientists themselves. It'll take both working together to change the incentives and solve the problems. But it can be done.