Just as a general note re repeated sig testing errors: Wouldn't it be possible to run a standard A/B testing run over a small but not insignificant number of it

Just as a general note re repeated sig testing errors: Wouldn't it be possible to run a standard A/B testing run over a small but not insignificant number of iterations, and then iterate over that a number of times? You could then use bayes to find a final estimate of, say, H1. As each high level iteration is fairly small, feedback can be provided to the user, although it couldn't be acted on. Speaking of which, if we have an expected number of false positives for any given number of test scores, couldn't you take the average number of positives generated as an rv and then try and determine if it is different to the expected number of false positives? It seems as though this type of error relies on the fact that a single false positive stops the testing rather then continuing on and allowing regression to the mean. By stopping this, it should then stop, or at least reduce this type of error.