The key items are not "real" inventory – you can't put things in there, you can't take them out, you can't rearrange them. They only exist because your current quest status tells the game that you are carrying the item, and it will vanish if you abandon the quest.

The space only exists because of the layout of the inventory window versus how many tabs are actually available.

Also, while it takes some amount of deliberate scheming to do so, it is entirely possible to be carrying enough key items to require all three pages:

https://www.reddit.com/r/ffxiv/comme..._of_key_items/

(I need to do a follow-up on that one; Dawntrail gave me more ammunition with three-item sidequests and I need to see if I can fill the third page yet...)

Feo Ul wasn't kidding when they went on that rant about our bag contents.