It healed him a little bit though so it didn't fail. It just wasn't strong enough to heal him all the way. So once again you are wrong.
"It was nearly as painful as it looked, but it was as if I could feel some of the corruption being burnt away from within my body."
So Eonar gave Alexstraza the power over life but not the ability to heal at all? Alexstraza doesn't have to be bound to the dream to have the same source of powers. That is like saying all mages have to be Titans because they draw upon Arcane power as well.Yesra and Alex having the same source of there powers is supported but just like all the other example's the idea that just having the same source of power gives them the same powers is unsupported as your own Twilight of the Aspects quotes prove as Alex is not bound to the dream and and do what others can not.