The problem you're describing there is a public policy one, not something to do with the scientific community. Public policy should be implemented with a trial at the start and a "check for effectiveness" step at the end because there is no way to guarantee the research it is being based on is accurate. Statistically, we expect a big chunk of research to be wrong no matter what level of integrity the scientists have.
"Statistically, we expect a big chunk of research to be wrong no matter what level of integrity the scientists have" - that's the actual problem under discussion here.
Research is heavily funded because people believe it's something more than a random claim making machine. You say governments should assume research is wrong and then try to replicate any claim before acting on it. But you end up in a catch 22: if the research community is constantly producing wrong claims there's no reason to believe your replication attempt is correct, as it will presumably be done by researchers or people who are closely aligned.
Additionally inability to replicate is only one of many possible problems with a paper. Many badly designed studies that cannot tell you anything will easily replicate. A lot of papers are of the form "Wet pavements cause umbrella usage". That'll replicate every single time, but it's not telling you anything useful about the world. Merely trying to fix things with lots of replication studies thus won't really solve the problem.
Research is far better than a random claim making machine even if some of it has errors that have caused the replication crisis. It's easy to overstate the level of the problem even though it's fairly severe at this point.
"Wet pavements cause umbrella usage" is something where I'd want to see your specific examples because it's easy to get a correlational study of that nature but very hard to design a causal one. The correlational studies are usually accurate and often useful for other research.
