The original idea came up from here:
Show how many times and on what difficulties you've done the quest
In the above link the main idea was for showing information in the window which appears when you press P.
This thread is a suggestion for Quest Window.
The number of completions is interesting not just for keeping track of XP, but also for your own statistics.
Ransacked chest timer shown is for the last ransacked chest.
Other chests timers are present too, but they change only the number of ransacked chests.
A similar window could have Raids too, with the raid timer included.
But it seems that the raid timer is for the quest giver, not the quest.
It could be in Quest window too, with OK button disabled until timer goes off.