The most annoying thing of all is that Blizzard actually had this EXACT same problem before - and they actually fixed it really fast. Then there's the specific dungeon factor, as some dungeons are a nightmare because tanks or healers need their legendaries from non-endbosses there, making places like the Sanguine Depths incredibly frustrating.

What's worse is that sometimes you get players that need an early, they drop out, you get new ones, and then they either immediately leave because they needed the killed boss or do 1-2 more bosses to get theirs then leave. Since some of these legendary memories drop from the first or second bosses, this can be especially frustrating, and even if it's 'just' DPS dropping out, sometimes it can be ALL the DPS, and it still messes with the run, despite the relatively short wait time.

A common tactic is to simply go tank or healer for a fast queue to get your DPS legendary memory and then drop. While this may not be a huge issue if a DPS drops out, as there's always more waiting in the queue and the additions are pretty fast, when a tank or healer does this, it creates some major problems. Blizzard has put legendary memories as drops from various bosses in dungeons, with relatively low droprates and, as you'd expect, players are immediately leaving after (not) getting their drop. This is one of those issues that you've probably come across yourselves, if you've ever done some random group finder dungeons.

Dungeon quest legendary drop rate