Damn lol reading your comment halfway i was hoping to finally having found a solution for this but it seems it wasn't.

FFXIV is a great game but there are things like this that absolutely don't make sense at all or have a reason to exist. When i started doing the guildhests i just read the text in dutyfinder right before or while queing for it. If you start reading the pop up when arriving in the instance and due to how quickly some are done the other players may already have cleared it while you're still reading. I also often play in my laptop without a mouse and its annoying to have to click that thing away that takes half your screen before you can start playing.

In kind of the same way i find the loot system very unpractical too. You get a pop up on which you have to click to open a window to finally see the loot, click need/greed then reclose the window. How many times did i not end up arriving late at next boss in raids because while looting i had to stop walking etc... I know WoW is kind of a taboo word here but the loot system was great. A little pop up window for each piece of loot that you could click on the fly and you were done. Simple and effective.