I don't like these kinds of features because they're not gameplay, they're RNG, and they're the kind of cruft found in mobile games to make up for lack of development skill. There are tonnes of mobile shovelware out there that has less gameplay than games from 1988. Since the mobile space is basically designed around freemium "trade time for money" cash grabs, there is a reason why these kinds of things are fundamentally rubbish.
If I select a retainer venture, airship venture, squadron mission, etc. I expect to be able to play something, not come back in 18 hours to see if I win the RNG lotto. I would not be surprised if these mini-non-games in the CN/KR version cost money to trade off time, and exist because of that market.
The Duty Recorder was something introduced too late into the lifecycle of the game. It is still the only way as PS4 user can do anything remotely like what some pc players do with unauthorized tools.
It has two uses that SE kinda missed the boat on
1) Machinima, this kind of thing would have made "Final Fantasy XIV: Dad of Light: Season 1" that much easier to produce, as the game engine could be used to play back any arbitrary combat or overworld data, and to make "cleaner" videos, one could change NPC's or players to protect their privacy or exaggerate a gag or something.
2) Combat replay, which is what it seems like it was designed for, but someone could produce an unauthorized tool to record all the incoming packet data and then play it back on the client offline and accomplish the same thing. Since the current version is tied to the maintenance cycle, it seems like it literately does something like this, where it's playing back the data as it was recorded, and is thus not compatibile after maintenance due to whatever minor adjustments or cleanup is done.
The Duty Recorder could easily be the next best thing for video producers the game has where you could play the Duty on the PS4, and then replay it on a PC at 4K later to produce your youtube video, and have the game client render the video slower and higher quality than recording it live would.