I like to think that the red deer was chosen because it nicely fills hole in the basegame and didnt require too much work.
The base game has no deers and no real european animals making the red deer the perfect animal to fit both of these spots.
In addition to that they didnt have to build it from the ground up since the fallow deer already had all the nessecary animations
And third, there was already scenery for it in place.
I really hope this years anniversary animal follows along theese lines
Something i would really enjoy for this year would be a squirrel monkey since it has pretty much the same situation going on as the red deer:
The basegame has only 2 habitat animals for south america, one of which doesnt even really count imo. And there is no classic monkey in the base game, i know we got the mandrill and macaque, but those dont give the same vibe.
Ironically both of those areas, SA and monkeys are still lacking even if you have all DLCs.
And lastly there is a monkey silhouette sign