Once you start discarding runs, doesn't that count as lying about the data/experiment? As in effectively equivalent to flipping the coin and only reporting it if it lands on heads?

In any case he does mention it won't fix all the problems but that it can clean up some of them and make addressing other problems a bit more straightforward. With p-values, sometimes even honest experiments end up with misleading conclusions. It takes a decent amount of complex understanding to perform properly, while something like gathering data and doing a conditional probability calculation has presumably less risk of honest mistakes