Seeing the problems with Duty Finder at 50 require you to know how FFXIV's current "endgame" content works. At 50, there are vendors that sell items for two types of tokens. "Darklight" items are item level 70 and require "Tomes of Philosophy". "AF2" or "AF+1" items are a higher item level (can't log in to check exact number) and require "Tomes of Mythology".
There are 7 level 50 locations accessible via duty finder:
CM - Second-to-last story dungeon. 8man. Drops no loot, but gives 100 Philosophy.
Final story dungeon. 8man. Long, filled with cutscenes, a few difficult fights. Nobody farms it.
Wanderer's Palace. 4man. Drops item level 55 equipment, weapons barely superior to Grand Company weapons. Gives ~50ish Philosophy.
Amdapor Keep. 4man. Drops item level 60 equipment. Gives 80 Philosophy. Gives 40 Mythology.
HM Ifrit, Garuda, and Titan all drop only weapons, but are also part of a relic weapon quest that gives you the best weapon in the game, so sane people only ever defeat each of the HM primals once (and then only ever go back when an acquaintance needs their quest completed).
This leaves AK as the sole piece of accessible, repeatable content to get gear. The terrible duty finder system can only accommodate X number of copies of a particular dungeon, and so if you queue for AK, even with a tank, or a healer, or even with a full party, the duty finder system will hang at "reserving instance" for 1-50 (yes, 50, not a typo) minutes depending on time of day and general population. It's literally the only thing in duty finder that people can and need to run repeatedly in order to get the best equipment. If you queue for any of the lesser (and therefore kind of pointless) dungeons, you do get in instantly, because most of the playerbase is concentrated in the one important dungeon and so there's plenty of room for CM and WP instances.
The final kicker is if you have a partial group, and the duty finder has matched you with an as-yet-unmet stranger, that stranger withdrawing from the queue will put your group back at the bottom of the list for instance reservation. Our FC has two tanks and so we were running two AK groups, neither with a healer. My group queued a split second before the other group because one of their members was AFK. Both groups were paired with a healer and sat at "reserving" pretty much the instant we respectively queued. Ours popped after 20 minutes, and the pug healer withdrew. Our other FC group then IMMEDIATELY popped their queue, and all entered. Meanwhile, my group sat for another 20 minutes before a new instance was available.