Why couldn't Aragorn become one of the Eldar?

Question

Canonically, Arwen elects for a mortal life, linking her fate to the Doom of Man. In doing so, she's the second elf to do so, after Luthien Tinuviel. My question is this: Why couldn't Aragorn have been granted immortality, and have his fate tied to the Firstborn? There is precedent for this as well--Luthien and Beren were not the only inter-species marriage in history: Luthien's parents were an Elf and a Maia (both immortal, and therefore irrelevant), and Luthien and Beren's granddaughter, Idril Celebrindal ("half-elven" in the same was as Elrond but counted among the Eldar) married a human (Tuor, son of Huor). Interestingly, both Aragorn and Arwen are directly descended from all three of these couples. The important note is that Tuor was able to become counted among the Eldar, due to his marriage to Idril, and his abiding love of Elvenkind. Couldn't the same have happened for Aragorn?

Other Notes:

I understand that thematically Aragorn represents the coming of the Dominion of Men, so his Fate is sealed, so to speak. And he may well have felt more kinship for Man than for Elves. But in-universe, would he have had a choice? Could Arwen and Aragorn have talked things through and decided that either mortality or immortality was right for them and their descendants? Or was Arwen choosing mortality really the only way their fates could have been linked? Could he have ruled as king for a reasonable span of years and then taken a ship into the West with Arwen?

Answer 1

Aragorn did not have a choice, his fate was tied to that of Men.

One thing you seem to be misunderstanding is that because Arwen and her siblings were granted the choice, all the descendants of Elros must have been as well. This is however incorrect. The choice given to the children of Elrond was a special condition bestowed by the Valar. After Elros' decision, his children and descendants were tied to the fate of Man, although they were given a longer life than most.

But to the children of Elrond a choice was also appointed: to pass with him from the circles of the world; or if they remained, to become mortal and die in Middle-earth. For Elrond, therefore, all chances of the War of the Ring were fraught with sorrow.
Elros chose to be of Man-kind and remain with the Edain; but a great life-span was granted to him many times that of lesser men.
_{The Return of the King - Book 7, Appendix A: Annals of the Kings and Rulers, I - The Numenorean Kings, (i) - Numenor}

Tuor's acceptance in the Eldar and his immortality

It must be remembered that Tuor is a very special case. Tuor was a troubled youth raised by the Elves of Mithrim, after spending a few years as an outlaw and a thrall, Tuor was chosen by the Vala Ulmo as his instrument. The Vala Ulmo guided Tuor to the shores of Belegaer, the first of the race of Men to do so, and from there on to Vinyamar and Gondolin. Tuor was sent by Ulmo to warn Turgon of the fate of Gondolin, that the Doom of Mandos was nearing fulfilment, and that he should flee. Although Turgon ignored the warning, Tuor remained in Gondolin and married Idril, Turgon's daughter. After the fall of Gondolin, Tuor and Idril fled to the Mouths of Sirion for a time before leaving for the west. Tuor's immortality was granted to him by divine intervention, given by Eru Iluvatar himself.

Immortality and Mortality being the special gifts of God to the Eruhini (in whose conception and creation the Valar had no part at all) it must be assumed that no alteration of their fundamental kind could be effected by the Valar even in one case: the cases of Lúthien (and Túor) and the position of their descendants was a direct act of God.
_{The Letters of J.R.R. Tolkien - Letter 153: To Peter Hastings}

In the same letter, Tolkien makes clear that such a choice was not granted to the descendants of Elros, and Aragorn therefore had no choice.

Elros chose to be a King and 'longaevus' but mortal, so all his descendants are mortal, and of a specially noble race, but with dwindling longevity: so Aragorn (who, however, has a greater life-span than his contemporaries, double, though not the original Númenórean treble, that of Men).
_ibid.

This, however, does not mean that it was certain that Aragorn's fate would be tied to the fate of Men, although it was certainly very likely, the case for Tuor was only supposed to be unique, never having been confirmed to being unique:

...and 'it is supposed' (not stated) that he as an unique exception receives the Elvish limited 'immortality'...
_ibid.

Answer 2

In the Silmarillion, Eru speaks of death as "a new gift" he has chosen to bestow upon men.

Given that Eru sees it as a gift, it's probably whole lot more acceptable to grant that gift to a few who didn't originally receive it, than it is to withdraw it from others who received it as their birthright (regardless of how much or little they might want to receive this particular gift).