You can also keep killing it every turn to prevent decking out and with only 2 def, Eagle Eye would be perfect for this. I'd consider raising the cost by 
at least, but I do like the overall idea.
eternity counters decking out with a 2-cards combo so i cant see how having another, more specific 2-cards combo would be an issue (which odly enough is in the same element)
I don't think air could have an ability like this, I prefer it to be in aether or time because of reincarnation and divinity.
yes, my planned fix (if deemed necessary by a Card Curator) is something like this:-
| Name | Homing Pigeon |
| Cost | 2 |
| Atk|HP | 4|2 |
| Text | Retrace:
Absorb  , return to the deck instead when it dies.
|
the worded ability is static, like Minor Phoenix's rebirth
but works like Flooding in that unless the condition is met (absorbing 1
when it dies), it wont get shuffled back into the deck
but that also means it can be nulify by other means such as lobo effect
