[Legate of Amon Lanc]

I think it's pretty clear. Two things which I agree with have been already mentioned - first, that only Ilúvatar really knew completely, and then secondly, that Men were supposed to take the role of Eldar after the Eldar faded. Obviously Men had many strange gifts, even the Eldar were amazed how much were they able to do, despite their pitifully short life, and how much effort were they able to put into things despite (or, of course: because of) their pitifully short life. That's obvious and it gives a lot of potential - of course potential to make good things as well to make a mess, but that's the fundamental choice that underlies the lives of Men.

And then, of course, and very importantly, there is the Second Music, in which the Men are going to participate alongside the Elves. And this, I think, goes once again back to one recurring theme in Tolkien's works in general, the powers of Man as a "subcreator" - and I am pretty sure this was in the background also here and also under the imagination of the "Dominion of Men" (so it's not only a matter of something beyond the world, but also within Arda, of course). Never in Tolkien's works was ruling something (when used in the positive way*) meant as controlling something, and he'd probably be in tune with the fundamentally Biblical purpose of Man whom God had set in the garden of Eden "to work on (could be even understood as "serve") it and guard it" (I think the King James Version has very nicely "to dress it and to keep it") - i.e. as a ruler, he is not to control things and use them according to his own whims, but to take them as a matter of caretaking (stewardship...). However the aspect of "enrichening" in Tolkien is even stronger in relation to Men (the role of caretakers is often given to other beings, like Ents, but after they diminish too, the Dominion of Men obviously comes and then all the responsibility probably passes to Men as well as everything else).

*Note: It was Saruman who boasted about "Knowledge, Rule, Order" obviously in totally twisted sense, but I can well imagine that all these terms were originally part of his "mission briefing" in their positive sense: Knowledge as understanding, Rule as caretaking, Order as preservation against totally unchecked - and therefore dangerous - chaos.