There HAS to be the cheapest time to purchase a ticket on average. The problem is that it is only relevant looking backwards and changes depending on if you look route specific, day time specific, domestic, international , advance purchase, how long the stay is, RT or OW, open jaw, or try to look at all fares filed and then it changes depending on how long a time frame you look at.

When there are dozens of articles that all say that a different time is the best time to book, it's highly probable that "the magic hour" changes so much depending on your parameters that it is of zero predictive value.