It could just be abolished. If the NSF was scrapped, what would the scientific world look like? Probably like the world before WW2, when most science was done by hobbyists or "inventors". Einstein did his seminal work whilst a patent clerk, etc etc.
Most analyses of the problems in science are really analyses of the problems in academia. There's no iron law that states academia has to be funded to the level it is today, and for most of history it wasn't. And let's recall, that these meta-studies are all about science, which is one of the better parts of academia. Once you get outside that into English Lit, gender studies, etc, the whole idea of replicating a paper ceases to be meaningful because the papers often aren't making logically coherent claims to begin with.
A lot of people look down on corporate funded science, but it has the huge advantage that discoveries are intended to be used for something. If the discovery is entirely false the resulting product won't work, so there is a built-in incentive to ensure research is telling you true things. The downside is there's also no incentive to share the findings, but that's what patents are for.
Of course a lot of social psych and other fields wouldn't get corporate funding. But that's OK. That's because they aren't really useful except for selling self-help books, which is unlikely to be a big enough market to fund the current level of correlational studies. That would hardly be a loss, though.