You are putting words in my mouth. I never claimed that Manwë and Morgoth would go head to head, but for some reason you get that impression. Because I wrote "one might need someone of equal power to truly challenge his existence" (granting that the equal power isn't 100% correct), doesn't mean that they´ll have some great fistfight.
The following quote does state that it will not be Manwë that will be the end of Melkor/Morgoth, but Eonwë. From The Hiding of Valinor:
"For ‘tis said that ere the Great End come Melko shall in some wise contrive a quarrel between Moon and Sun, and Ilinsor shall seek to follow Urwendi through the Gates, and when they are gone the Gates of both East and West will be destroyed, and Urwendi and Ilinsor shall be lost. So shall it be that Fionwë Urion, son of Manwë, of love for Urwendi shall in the end be Melko’s bane, and shall destroy the world to destroy his foe, and so shall all things then be rolled away."
To confuse ourselves even more, the prophecy of the last battle states that it is Turin who will destroy Morgoth. From the early sketch of the Silmarillion:
"When the world is much older, and the Gods weary, Morgoth will come back through the Door, and the last battle of all will be fought. Fionwë will fight Morgoth on the plain of Valinor, and the spirit of Túrin shall be beside him; it shall be Túrin who with his black sword will slay Morgoth, and thus the children of Húrin shall be avenged."
And a very similar piece from the Shaping of Middle-Earth confirms that Turin will do the job:
"Thus spake the prophecy of Mandos, which he declared in Valmar at the judgement of the Gods, and the rumour of it was whispered among all the Elves of the West: when the world is old and the Powers grow weary, then Morgoth shall come back through the Door out of the Timeless Night; and he shall destroy the Sun and the Moon, but Eärendel shall come upon him as a white flame and drive him from the airs. Then shall the last battle be gathered on the fields of Valinor. In that day Tulkas shall strive with Melko, and on his right shall stand Fionwë and on his left Túrin Turambar, son of Húrin, Conqueror of Fate, and it shall be the black sword of Túrin that deals unto Melko his death and final end; and so shall the children of Húrin and all Men be avenged."
It seems, that Tolkien must have considered it possible for both Turin and Eonwë to kill Morgoth (why Manwë then couldn't have done the same is beyond me), though, Eonwë get's to do the honourable task in the final version of the Battle.
In the Silmarillion Turin get's to kill a dragon instead:
"The language of the Folk of Haleth was not used, for they had perished and would not rise again. Nor would their tongue be heard again, unless the prophecy of Andreth the Wise-woman should prove true, that Túrin in the Last Battle should return from the Dead, and before he left the Circles of the World for ever should challenge the Great Dragon of Morgoth, Ancalagon the Black, and deal him the death-stroke. "
However, that does not diminish the role of Manwë in the entire thing.
"Manwe will not descend from the Mountain until the Dagor Dagorath, and the coming of the End, when Melkor returns".
If Manwë descends from his Mountain onto the plains of Aman (where the battle takes place) it must have some great significance, especially, if he does it at the time that Melkor returns.
Let's take a look at a few undebateable facts:
1. Manwë sends Eonwë to take care of The First Dark Lord.
2. Manwë sends The Istari to take care of The Second Dark Lord
3. Manwë sends Eonwë again to take care of The First Dark Lord when he returns.
4. Manwë descends from his mountain when the final battle arrives.
It seems obvious to me, that Manwë is the source of resistance against Morgoth, and as such the battle is more a matter of Manwë vs. Morgoth, than of any of his minions vs. Morgoth, though many of them have BIG parts to play in the battle aswell (like killing him).