Would be nice, but where would the money come from? Even if you live in a country with high taxes that fund ridiculous projects, they are still often accountable to the public. Would the public want to fund new research or try to replicate or disprove other studies? The only way to make it work would be to build-in a certain percentage of funding for such a purpose in reaction to some gross oversight, so you could get the public behind it, or perhaps get some wealthy donors behind the cause, but I think you'll have a difficult time.
The better option might be having research students be required to replicate at least one study that hasn't been replicated in addition to doing their own research. That way you get some free labor!