My thought is that by checking once or multiple times, you are potentially catching noise rather than signal - for example, you might have luckily/unluckily gotten 100 death events (an abnormally large effect size), but in the long run, those probabilities are going to settle to what they expect. I recall asking this question several years ago to one of my stat professors and he drew a line indicating the effect/signal over time and variation going above and below that line, indicating that if you glanced at one of these earlier timepoints, you would be likely to get misleading conclusions. In the extreme case, one could imagine unethically checking the results of the trial many times and cherry picking the significant results (hence the need for multiple hypothesis testing corrections).
A related StackExchange question is here. How does doing an interim check for data safety/monitoring impact power (ability to detect effect if there is indeed one)?
