I DO think Demandred is almost a Dragon in terms of his ability - because multiple sources have conveyed this very fact to us. He WAS almost the Dragon. The second greatest man of the Age of Legends. FACT. That accurately depicts my point of view, indeed.
Ishamael was the Dragon's arch nemesis, the man who drove him to his death, the man who is, for the Shadow, what the Dragon is to the Light.
No doubt it is Demandred's greatest wish that the Dragon should die at his hands. But Moridin thinks that the resolution of this conflict, and the final victory of the Shadow, depends on his meeting with and defeating the Dragon. This has been foreshadowed since the prologue of the Eye of the World.
For one, it is the personal obsession of a lifetime, for the other, it is destiny and is bound up in all his beliefs. I cannot see how you think the former outweighs the latter.

And yes, as things stand, Moridin may well die when Rand does. But who's to say things will remain the same? More importantly, who's to say Moridin cares about dying? What does death mean if by that death you ensure the destruction of the Wheel and are freed from the cycle of rebirth, which is what Moridin wants? Who's to say the DO hasn't promised to snatch his soul and have him revived immediately?

And a Demandred vs. Mat situation makes sense. The man who did betray the Dragon against the man who might have, in another life. Mat too, at one point, was jealous of how much importance people gave Rand. Mat is the foremost general of the Light, as Demandred is of the Shadow. More importantly, Mat can handle Demandred because his foxhead medallion can offer him some protection against Demandred.