It has already been pointed out in BMWurm’s answer why neither elf nor wizard considered trying to take the ring west sensible, and that the peoples of Middle-earth would have to deal with the ring by themself, eventually, because Valar intervention would not be an option: “And they who dwell beyond the Sea would not receive it: for good or ill it belongs to Middle-earth; it is for us who still dwell here to deal with it.” Still, this doesn’t explain why that is the case — and the reason for it is, in my opinion, is the real answer and the most important fact, being directly related to the entire genesis of Middle-earth.
As we have already seen in the past, each Age was related to one “scale” of epic conflict — while the First Age was an obvious “Epic-est Fight of Valar & Elves vs Melkor”, with the greatest scale of both conflict and damage, the Second Age was “Epic-er Fight of Elves & Humans (Númenóreans) vs Sauron”; on the other hand, the Third Age was “Epic-ish Story of Couple of Battles of Humans & what’s left of everybody else vs what’s left of Sauron” — it’s the obvious road to the concept of the Dominion of Men that would follow in the Fourth Age. That was the plan of Eru from the very beginning, and, obviously, it required Men to deal with the remnants of the past to forge their future, one way or another. As such, while divine intervention was not only possible, but happened as a straight fact (Great Eagles' help, Gandalf being reborn, etc.) — it was Men (well, in a strange alliance with all the remaining sentient races of Middle-earth) who finally defeated Sauron (in the military sense) — and the Hobbits who won the fight in the broader sense — as such, fulfilling their destiny by setting their future. Yes, it was their destiny to create their destiny — as opposed to the Elves, obviously.
Also, note that this is strictly parallel to the storytelling aspect of any epic work — signifying that it’s not only an in-world reason, but an artist’s reason too — it happened the way it should happen to make the most of the story — because the story was meant to go the most expressive way (see other epic works, from Homer for example). Also, see Tree and Leaf — as JRR Tolkien explains this concept there to some extent, being parallel to Jesus Christ’s death — it has to happen, because it’s for greater good and because God has planned it this way. To extrapolate (since Valinor was a “heaven” of sorts from Human point of view) — asking The Ring (the source of sin) to be taken to Valinor was similar to asking God to take away sin/plague/some source of evil from Earth to Heaven — it was impossible, because it would, in a way, rob Man of their destiny to forge their free will.
Therefore he willed that the hearts of Men ... should have a virtue to shape their life, amid the powers and chances of the world, beyond the Music of the Ainur.
NB: if somebody would be so nice as to provide me with some more source citations (I’m too lazy/busy to dig for them) to back it up, I’d be very grateful.
Valinor was not an option, because Eru explicitly made it Man’s sole choice/possibility to be able to forge their destiny by defeating Sauron in the Last-est Alliance of Middle-Earth — bringing The Ring to Valinor and throwing the potato at Elves/Valar was thus not an option.