Why would Manwë make himself sit on his throne for all eternity until Melkor comes back?

Question

Before the War of Wrath, Manwë Súlimo King of Arda, Lord of the Valar, and caretaker of Valinor Untouched and Melkor were brothers and the most powerful but wanted different things in life, like Melkor weaved Evil into Arda and Manwe sought peace and commerce and even walked amongst the Elven species and held conversation with them (most famously his Speech to Fëanor about restoring Yavanna's Trees). He was refused the Silmarils by Fëanor because Fëanor loved them too dearly. After Manwë and the other Valar kicked Melkor out into the Void forever he vowed to remain in his throne until the last day of Doom when Melkor will destroy the Door of Night,Sun and the Moon, Rescue Ar-Pharazôn from the Caves of the forgotten and be challenged by Turin Turambar and killed by him.

What's the reason behind this?

It seems rather odd that he would commit to an act of righteous commitment until the end of the world. Is it because Melkor was his brother? And he wanted to bide his time by taking a vow of paralyzation until the Time had come for Dagor Dagorath?

Answer 1

The Valar agreed to remain in Arda until the end of the first music (the first stage of the world) before it was shaped. When Melkor sang his discord, the Valar agreed (primarily Manwe), to take their own songs and play it out to decide who was right.

Eru granted them space (with some rules such as The Flame Unperishable), and Arda was formed. The final battle is Dagor Dagorath, and it is prophesied that Melkor will escape the Doors of Night and lose. The Second Music will play, and it will be greater than the first (a new world with no embodiment of evil).

So basically they're still on Arda, because they still haven't defeated Melkor yet, which they agreed to do before returning to the Timeless Halls with Eru and all of mankind.

Answer 2

The Valar—that is, those of the Heavenly Powers created by Ilúvatar who had chosen to go into Eä, the physical universe—were restricted to Eä either by their love for the universe or by Ilúvatar's command:

of the Ainur some abode still with Ilúvatar beyond the confines of the World; but others, and among them many of the greatest and most fair, took the leave of Ilúvatar and descended into it. But this condition Ilúvatar made, or it is the necessity of their love, that their power should thenceforward be contained and bounded in the World, to be within it for ever, until it is complete, so that they are its life and it is theirs. And therefore they are named the Valar, the Powers of the World.

(Silmarillion, "Ainulindalë")

Manwë did not swear to "remain on his throne", certainly not in the sense of "sitting in one place forever", after Melkor was driven into the Void. Of that event the Silmarillion says only:

But Morgoth himself the Valar thrust through the Door of Night beyond the Walls of the World, into the Timeless Void; and a guard is set for ever on those walls, and Eärendil keeps watch upon the ramparts of the sky.

(Silmarillion, "Quenta Silmarillion", Chapter 24, "Of the Voyage of Eärendil and the War of Wrath")

Manwe's throne is mentioned several times in the Silmarillion, but it is never said that he "remains on his throne"; one could say this by metonymy, in the sense that he remains "as king of the physical universe"; but I don't think this is what you had in mind, and it doesn't imply any sort of "vow of paralyzation".