Publishing all of the studies would not help with the false positive rate itself, but it would help immensely in making accurate decisions about what we should set the p threshold at. If we want a certain false positive rate in a field, we can engineer that rate if we know going in what is the probability that an alternative hypothesis is true. That probability is really hard to determine when all studies are not published, and this is a separate and contributing issue to replication crises in certain fields.