I'm not really willing to give the story the benefit of the doubt when it repeatedly held Jake up as special and heroic without demonstrating any character traits that justified him being treated that way by the other characters, including Eywa. And even if you go with that rationale, it still begs the question of why they recruited Jake in the first place. This is a scientist gig, why are they putting a grunt soldier in and doing so with no training and no job other than to act as bodyguard - on a planet where they've been studying for a generation without needing an Avatar bodyguard? To say the Na'vi and Eywa's interest hinges on his warrior status just puts focus on the highly contrived and fairly illogical way in which Jake is brought into the Avatar program to begin with (which is about where the movie lost me, with subsequent points such as his irresponsible behavior merely serving to make me find him an increasingly ridiculous character). As for how sentient and aware Eywa was - She was just as sentient and aware as the story needed Her to be when it needed Her to be without bothering with any consistent world building. To me it's all just bad writing.
You know, it's funny, but the more we debate this, the more I feel that Jake
isn't the contrived character that you think he is - I still think a lot of the
story is contrived, but not necessarily Jake himself, at least not to the same extent that you seem to.
We're clear that the avatars are a scientific, sociological tool - not necessarily a
logical one, but okay, I can give them that having a physiology that can blend in harmoniously with the natives, rather than a 'tiny' human body that must constantly be insulated from the environment, could be a very big advantage in understanding not only the Na'vi, but Pandora itself. The illogic comes from the idea that a for-profit company whose primary effort is to mine the planet/moon would even bother with this, unless there were some hugedacious PR benefits to come out of it, and I just don't see that they would.
I don't see why there is any question about why they 'recruited' Jake - they wanted some sort of return on their investment in the avatar, and someone may have been smart enough to realize that having a soldier in there could be useful, especially since it was made clear
from the start that Pandora was a hostile environment, and their efforts there were engendering hostility from the natives (tires full of arrows, anyone? The Na'vi were already resisting). Maybe the avatar-based research program wouldn't be a very sound investment for PR purposes, but if news got back that they were shooting down the natives with choppers and powersuits, that would surely cause some protests back home, so since they
already had a body in progress, why not see if they could get some security a little closer to the action that wouldn't totally screw them politically? I can buy that, and it doesn't need to be specifically stated just to make sense. I don't think the unique nature of this one avatar makes the Na'vi or Eywa's interest seem contrived - if anything, it gives it more of a basis for plausibility. We just didn't realize he was unique when the jellyfish seeds descended upon him - but apparently, the world-mind
did. Even though she wanted to kill him at first, even Neytiri admitted that he was different from the other sky-people and avatars - she'd never have expected Grace to tackle the creatures of the night, and warriors often look down on 'helpless' intellectuals the same way intellectuals look down upon soldiers. She could see that Jake, despite being an outworlder, had something in common with her people - he was a fighter. A childish
moron of a fighter, but at least he wasn't a childish moron of an
intellectual 
. No matter how much the Omaticaya might like Grace and the others, they were still not warriors like The People.
I honestly never saw Jake 'held up' as heroic, either by the story or by the other characters. Of his own people, the only respect he earned was for sticking with life even after he lost his legs. Among the Na'vi, he was as much a burden as anything, until he finally learned how their customs worked and how to carry his own weight - hardly a "heroic" depiction. He was just barely accepted, certainly not admired, and the only way he ever managed to finally impress them was to saddle Toruk, using, as others have noted, a decidedly non-Na'vi approach, one
they didn't know about. He cheated, but it was in the cheating that he finally
did become worthy of respect: he did it because his eyes had been opened, he was looking beyond his own needs, and he knew that the only way to help them was to get them to help him, by becoming one of their legends reborn. Sure, he tricked them, but he tricked them for very good reasons, and whether they found out or not, he accomplished what he had to do: help the Na'vi save
themselves. Some call that "Mighty Whitey," but to me, that says something about bringing an outside perspective to a problem. Jake didn't save the planet - he saved himself by becoming part of something bigger, by providing a focus that allowed the planet and its people to accomplish what they might otherwise not have attempted, because it wasn't part of their nature to do so. He wasn't the lever - he was the fulcrum.