Take a hundred papers which claim results at p=0.05. At the asymptote about 95 of them will turn out to be correct and about 5 will turn out to be false.

No, they won't. You're committing base rate neglect. It's entirely possible for people to publish 2000 papers in a field where there's no hope of finding a true result, and get 100 false results with p<0.05 just by chance (along with 1900 other false results with p > 0.05).