No matter what clever theory we come up with, the real reason will always be that Bandai wanted to make the toy more marketable. Every other combo had gotten their own head-design.
The green-eyed hawk head was already used for the TaToBa combo, so Bandai thought it would be cheap to sell a new combo with the same head.
If you want a fan-theory, you could say that TajaDor worked the same way as Ankh's Greed form; If he didn't have enough medals, his face would lose the feathers, and he wouldn't have any wings.
None of the other Greeds had this side-effect. They only lost their armor if they didn't have enough medals. Ankh actually lost his physical features.
When OOO didn't have the full TaJaDor medal set, the hawk head would lose some of its physical features as well.