Present day reasoning about difficulties in science reproducibility, science governance, and the use of science for policy could benefit from a philosophical and historical perspective. This would show that the present crisis was anticipated by some scholars of these disciplines, and that diagnoses were offered which are not yet mainstream among crisis-aware disciplines, from statistics to medicine, from bibliometrics to biology. Diagnoses in turn open the path to possible solutions. This discussion is urgent given the impact of the crises on public trust in institutions. We ask whether the present crisis may be seminal in terms of drawing attention to alternative visions for the role of Science in society, and its relevant institutional arrangements. We finish by offering a number of suggestions in this direction.