National science funding might work if scientists were disbarred for publishing wrong studies too often or too flagrantly, or if they couldn't be verified at all.
Imagine Ancel Keyes being postumously stripped of his degrees and dishonoured, for example.
Imagine Jonathan Jarry M.Sc. having that M.Sc noped right off. Sorry, Science judge has ruled you incompetent. Dr. Ed Nuhfer? You're not a doctor, you're a fake. Dr. Patrick E. McKnight? Liar. Dr. Simone C. McKnight? Not a doctor, p < 0.00005. Dr. Phillip Ackerman? You're a useless screwup.
These people can barely be trusted to pilot a taxi, let alone a study.
For a little while, at least, "science" wouldn't be basically unreliable.