Atiesh, Greatstaff of the Guardian is going to be replaced by most everyone that has it in a few months by better level 70 epic weapons from 25 man raids.
It's pretty much a leveling/first raid dungeon weapon right now.

With all the lore surrounding it (staff of Medivh, greatest magic-user in Azeroth), do you think it'll rot or get upgraded?
Most of us have seen the Corrupted Ashbringer quest, which some say implies the existence of a Legendary Ashbringer in The Outlands somewhere. I hear it involves Nat Pagle, 425 skill fishing and the Dire Maul library, kek.
Atiesh does open a portal to Kharazan, which at the end of might contain a scared NPC hiding, willing to tell you more about Atiesh. Or not.

If you were working on the game, would you let Atiesh rot, since such a little percentage of your playerbase actually owns the item?
Would you create a level 70 weapon in it's stead and have Atieshes (Atieshii?) be upgraded by killing lastboss_01 of Really Hard 25 Man Raid Instance? (And would it be worth the forum uproar?) How powerful would you make it? (Best in game lvl 70 Artifact weapon, just another Epic etc...) When would you buff it?

It's either let it be; the guilds who have killed Kel Thuzad can have a few players running around with a very nice Legendary for a while that comes with in-game recognition as master boss killers, or prize them even further by being the few who have killed both KT and the last boss of an upcoming instance and receiving an even greater weapon.

I doubt they'll change it; they have no interest in making people go back and run old progression content in order to get new progression items, which is a good choice - imagine if Thunderfury had dropped in a level 50 raidtimered instance.

I think that it will not be buffed. I have come to this opinion because we have not yet seen a single upgrade for a legendary item, and the official forums have troughs of requests for such. Atiesh, effectively, becomes the cooler sibling to the Staff of Celebras, which is more than I can say for all the epics and other legendaries.

I'd also rather see new items than upgrades to old items.

Our only existing references are Thunderfury and Sulfuras, neither of which have had their actual item properties upgraded (TF's aggro generation giving it abnormal longevity, not its stats). My guess? remains the same.

No.