I don't think just all Swords absorb Haki, but all matter of objects can. I believe that's the secret of how the Poneglyphs were created. They weren't that hard, and then carved, but rather carved first and then hardened.
I think it has to do with a specific type of Haki that people can posses, which that only those who Specialize in armament Haki can achieve/use.
The Poneglyph point seems rather logical. I would have no issues admitting I was wrong about this haki absorption when it is proven.
I think the main issue is with other characters not having black blades specifically top tiers.
Now for the Oden haki Statement. We know Kaido knows what haki is. My issue is he specifically states Oden's Presence. Why didn't he just say Oden's haki which is something he has said before?
Even in the translations we have today, he never says Oden's haki
Also if Oden's haki was in the sword, wouldn't Zoro or Hitetsu have made a statement to that effect?