Before the Vulpera chain, I presumed that this was because the Allied Races weren't specifically joining each faction, but instead just acting as allies. That is, an Allied Race would be there to help out, but wouldn't have voting rights and really wouldn't be forced to do anything. Hence why they wouldn't need a Blood Oath. Though as you said, we haven't used it outside of the Taunka quest anywhere...the Blood Elves & Goblins never to my knowledge had to take that oath.
Given that the Horde no longer has a Warchief, one has to assume the Blood Oath is gone for good. I'd love to see Blizz replace it with a new oath, one that accurately reflects the council setup and talks about what to do in peacetime as well as wartime.