The rules are clear in several parts of the necessity of this but it makes no sense.
At first I thought the idea was to assure that the player did not necessarily know which cards were already drawn. But since the user does not make an educated guess of choosing the "correct" card, because the dice tell you which card to draw anyway.
Moreover, if you discard without looking, there is a good chance that you will unknowingly discard the Wild card, even though the player is supposed to be aware of how many jokers have been drawn, because if both have been drawn by the time you are at phase 12, the decks should be reshuffled.
Why can't I just discard face up?
First off - THANKS for giving the variant a try and for posting the gameplay pictures!
After looking over the rules tonight (it has been a while), I am pretty sure that the following is what I had in mind back when I designed AIR.
You are correct in your suspicion that the face down discard pile is one of the game's fog of war elements. You are also correct that this procedure does not serve to affect card play by the player (as the variant utilizes the card deck as a randomizing device rather than for card play as in the original game).
So why the face down discard pile?
Basically this adds to the fog of war by introducing additional uncertainty about when a country card may come back up (i.e., is Kamchatka buried as an initial discard or did it get dealt back to the top of a stack in the Draw Pile Renewal Phase?) As you note, this would not apply to cards that are discarded after being used by the player. However, the fog of war effect stems from two other rules:
1. When the Draw Piles are initially dealt out (the remaining two cards are discarded face down to start the discard pile - Setup, step 4), and
2. Each time the Draw Piles are renewed (additional cards are discarded face down depending on the number of Earthling Capitals still in play - Phase 12, paragraph D).
Since these "hidden" cards are used to start off the discard pile, it follows that the cards discarded during the other phases are also placed face down (even though they were viewed by the player).
Also, for clarification, please note that it is not a problem if one (or both) of the Wild Cards are unknowingly discarded during the aforementioned stages. This is because the Draw Piles are to be renewed in either of the following cases:
1. Both Wild Cards are drawn and used (which cannot occur if either one is among the "hidden" discards), or
2. When any Draw Pile is empty at the beginning of the Draw Piles Renewal Phase (Phase 12, paragraph B.)
Admittedly these procedures do not generate a huge fog of war impact by themselves. However, every little bit helps since uncertainty and challenge are the "meat and potatoes" of this type of solo game. Hopefully the procedures are minimally intrusive when compared to the additional suspense and surprise they can add to the game.
If you have any other questions or comments, please let me know!