He died well before that happen, he probably couldn't stop them if he wanted to.

I roleplayed that my character was weaponless in the Northern Wastes, and he ran for the tomb in hope of safety. In there, his Thalmor aggressors broke in, and my character was deeply wounded. He looked up to Ysgramor, and saw Wuuthrad. He pulled the weapon from the statue and struck the Thalmor down. When he turned to return the axe, it would not go back. He took it as a sign from Ysgramor that my character should be the next wielder of the Elf-bane battleaxe. He has finished his conquests, and awaits in his home, Wuuthrad at his side, awaiting the next Great War.

but.........Wuuthrad was a bunch of shards in the beginning and your character is responsible for gathering them to be reforged lol.

Not necessarily - if you play a canon Skyrim, then you could have a different character run the Companions questline and leave the axe in the tomb. Then you could have a different character run and find it.

RIght now I've got it stored in a Hjerem display case underneath Ysgramor's shield, but when the time comes to invade the Summerset Isle, oh excuse me, Alinor my dragonborn will take it with me to wipw the Thalmor from the face of Nirn. I think Ysgramor would approve.

I have it in a place of honour, in one of (the few) wall plaques in Breezehome, and as I'm Harbinger, I think that is a suitably respectful place. As previously noted, anyone could steal it from the tomb. I generally try to display the most significant artifacts of the area on the walls of the house that I own in the town. And at the same time being practical enough that if the weapon doesn't do the most damage of its type that I own, so it gets a passive honour (on the wall) not the active honour (of use).

Well in my game the damn axe always ends up on the floor when I reenter the place so I usually just take it back and leave it in the chest in his burial chamber along with his shield.

My main Nord doesn't loot the dead or their resting places anyway unless he needs a specific item for a quest.

How's that relevant? I was wondering the Northern wastes, and the Thalmor followed me there. I ran for the closest and (I presumed) safest place I could, so I went for the ruin, hoping I could hide.

I have two characters that finished the Companions storyline, and both took the axe. My 2-hander took it and used it: she felt it honored Ysgramor to use his weapon, especially against the Thalmor, whom she hated. My 1-hander couldn't use it, of course, but took it and displayed it in one of the display cases in the Harbinger's rooms; she felt it was better publicly displayed in the hall of the Companions who looked on Ysgramor as their founder and inspiration than in his tomb, which very few people would ever see. It would have been even better if you could display it in the same place of honor that the fragments were in.

No, it's not dishonoring to take the axe. Even if you are playing an Altmer (High Elf) you can use it to kill the Thalmor with. Some Altmer hate the Thalmor just as much as the Nords. For instance, talk to http://www.uesp.net/wiki/Skyrim:Legate_Fasendil and listen to his story.

Considering the current (sad) state of the Companions, I think the axe and shield are better off with anyone having the guts to wield them or with someone who rightfully decides to return them to Ysgramor tomb.