Why is it that in Tolkien's world, Men come after the 'first born' elves and take-over from elves as the dominant humans on Middle Earth?
In one sense this sequence of elves then Men 'had to' be true if elves ever were to be dominant, because Tolkien was writing 'feigned history' and his reader lives in a world of Men - where elves are either absent or hidden.
This sequence of first elves, then men - was indeed planned by Eru (God) - implying that it is A Good Thing for men to take-over - that it is better for the world to be run by Men than by elves.
Yet the reader finds this hard to understand, and Tolkien is never able to explain satisfactorily how exactly Men can be regarded as genuinely superior to elves* - given that elves are more beautiful and intelligent; better at magic and science, arts and crafts; do not suffer aging, do not get ill - and do not die.
Well, elves can be killed - apparently like Men; but there are brief hints (especially in the Tale of Aragorn and Arwen in the Appendices) that after death the spirits (or souls) of elves stay within the world (potentially to be reincarnated), while the spirits of Men leave the world - and go... somewhere else.
Yet again though; it is not clear why this is a superiority of Men - beyond that after some thousands of years, most elves simply get fed-up and tired of being alive - and therefore might crave extinction as a form of 'rest'.
Furthermore elves also care deeply for the world - they love and cherish nature. Knowing they will live in the world indefinitely, they preserve its beauties and (through their arts and craft) create new beauties. By contrast, short-lived Men seem to have the attitude of mere visitors to Middle Earth (or 'guests' as elves apparently term Men).
To explain the 'superiority' of Men, and why they replaced elves; Tolkien talks variously that elves are confined to the circles of the world while Men are able to 'escape' from them. But it is not obvious why this escape - into what? - is better than the elves chance to live 'forever' in undying paradise.
Or Tolkien explains that Men have, in some sense, genuine freedom to act outside of the music of the Valar - the destiny of the world. But again, it is not clear that elves lack anything of free will, at least as it can be observed. Legolas seems no less free than Boromir, or Galadriel than Gandalf - and their capacity to choose freely is indeed an important aspect of their goodness.
However, Tolkien was of course right - and the difficulties in explaining convincingly how and why Men 'superseded' elves arose mainly because he was trying to explain the superiority of Men without explicitly naming Jesus Christ, resurrection and Heaven.
The simple explanation of why Men came after elves, superseded elves, and are 'better' than elves - is that by dying - really dying - and leaving the circles of the world, Men are able to be resurrected into Heaven. The superiority of Men is just that and incarnated life in Heaven is better than life in paradise.
By not-dying, elves are doomed to remain essentially themselves - whether these selves are reincarnated or spirits. And no matter how superior elvish selves may be to mortal Men, they are greatly inferior to resurrected Men, who will excel even the Valar - since resurrected Men are cleansed of sin, and think and live in full accord with the divine will.
*Note: Tolkien's best discussion of 'elves versus Men' comes in The Debate of Finrod and Andreth. I have also found helpful a really excellent fanfiction novel called The Question of Pengolod, which I have mentioned before on this blog.