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.
"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.
There will always be cases of fraud if someone deeps deeply enough into large institutions. That doesn't actually indicate that there is a problem.
Launching in to change complex systems like the research community based on a couple of anecdotes and just-so stories is a great way not actually achieving anything meaningful. There needs to be a very thorough, emotionally and technically correct enumeration of what the actual problem(s) are.