I think it's a good idea overall - I'm a key hoarder and it'll save me some bag slots, as well as the fact that I won't have to remember to grab them out of the bank before heading to the dungeon.
It does make me wonder, though... Blizzard currently takes the stance that they don't want to spend time making content (eg. long quest chains) that are class-specific, or any other content that only a limited number of players have access to.
But... I can't imagine people who would make much of an effort to do difficult quest chains for dungeon keys that aren't needed any more... Basically making the content more limited than the class-specific quests, because people still do those (eg. the shaman totem quests, warlock demon quests, or the epic Rhok quest).
Personally, I think Blizz could - and should - make more content like this. Class-specific, or at least with rewards that are so desirable that even if you're 20 levels too high, you'll go back and do them.
As for the old, already-existing content... why not have a class-specific or attunements Achievements pane that doesn't give any points, similar to the Feats of Strength? Blizz spent so much time on the Onyxia attunement, for instance, that it seems a shame for people not to see it.