What can they do? It's an incredibly hard problem to solve. It's like asking why the buisness community has done nothing to adress the housing crisis.
Large scale culture changes, or the entire structure of the way science is conducted and funded, would be the only solutions
* working groups "red teams" whose whole job it is to find weaknesses in papers published at the university
* post mortems after finding papers with serious flaws exposing the problem and coming up with constructive corrective actions
* funding / forcing researchers to devote a certain amount of time to replicating significant results
* working groups of experts in statistics and study design available to consult
* systems to register studies, methodologies, data sets, etc. with the aim of eliminating error and preventing post-hoc fishing expeditions for results
The whole-ass purpose of a university is seeking knowledge. They are fully capable of doing a better job of it but they don't because what they actually focus on are things like fundraising, professional sports teams, constructing attractive buildings, and advancing ranking.
Most universities would be better off just firing and not replacing 90% of their administration.
That's because universities are in the business of teaching. Apart from a few rare exceptions, universities don't have the money to hire redundant people. Instead of hiring many experts in the same topic, they prefer hiring a wider range of expertise, in order to provide better learning opportunities for the students.
Statisticians can find faults in many studies. Universities even employ statisticians to act as consultants for research in other departments, as that raises the quality of the institution's publications.
Make peer review public. Weight replication studies more. Make conducted peer reviews and replications an important metric for tenure and grants. Publish data and code alongside papers.
It doesn't help. It just means outsiders get to read bad peer reviews and bad code, but the right people within the system don't actually care. There's no way for the public to hold anyone to account, science is a law unto itself because politicians are generally not scientifically minded. They can be easily bullied with technobabble. The few that aren't susceptible to this don't tend to rise to the top.
There's literally thousands of different things they could do.
But why do anything when the real business of academia is in the tax-free hedge funds they operate and the government-subsidized international student gravy train? There's no short-term incentive to change anything.