> A power analysis is how you determine reproducibility

All a power analysis does is reduce the chance that the result is a false negative. It doesn't reduce the chance of a false positive.

> False positives produce inflated effect sizes

Not always. Lots of studies publish as "significant" as soon as they get a p-value just under .05. Inflated effect sizes are certainly a sign that something could be wrong, but it's just one indicator.

Regardless, even if you have a power analysis at the conventional threshold of 80%, and a p-value of .05, you're still going to get spurious positive results 5% of the time, and spurious negative results 20% of the time, by definition.