A Question about speech

I've come across some work on free indirect speech/style recently, and have come up with  questions:
If our character's speech and thoughts are being filtered directly through to us by the narrator, what does this say of the omniscience of our narrator? If the narrator cannot then be omniscient in every aspect of the story, what does this say of the reliability of the narrator?

I don't care: I'm eating it!

These are big questions to answer, and I might not be the best person to do so, but it's buzzing through my head now, so I have to deal with it, for my own sake if nothing else.

Inherently, we must be able to invest some trust in our narrator. We depend on her to guide us through the story to elucidate for us enough to move the story forward without bogging us down in unnecessary detail or stream of consciousness to no purpose. She must, like our poor, overwrought hippocampus, help us to forget that which isn't important, while ensuring that everything essential is presented for assimilation into the narrative.

So, if our narrator is capable or reading the minds of our heroes, there can surely be no excuse for withholding anything from us? At that point, we cannot have mystery, twists or reveals without our narrator becoming somewhat untrustworthy and unreliable.

The Balance of Reliable and Omniscient

In order for our narrator to become both capable of free indirectness and being sufficiently vague on other parts of the story, they must be within the story. A friend of the main character might know them well enough to know what's going through their minds. Perhaps we're getting thoughts reported to the narrator later (at which point they become a second-hand witness). This puts them close enough to events to have proximal knowledge, but with the same restriction on not knowing everything that went on.

The problem here is that this narrator then becomes a protagonist, if not the main protagonist. How do we trust them to be unbiased on the rest of the story? (I've not had to worry about this in my own writing: my characters are ghosts whose emotions run off them like a physical force. Everyone knows what they're feeling.)

This differs from the 'unreliable narrator' which I will discuss in a different post. When the free indirect style is in use, we are suddenly aware of the author-as-narrator. Jane Austen used this style famously and would often directly address the reader during writing. However, she did so in the voice of the character who was also the narrator. The free indirect style gives us unfiltered access to the thoughts and feelings of the character, but spoken as though by another. Does this disjoint, where the narrator gains omniscience and it is shown to us, make it difficult to accept that the thoughts of others are denied to us?

Well, perhaps not if it is managed correctly. If the narrator is consistently the only power who shares their thoughts with us as directly as indirect free permits, then this becomes the cornerstone on which we base the narration. If indirect free is used for some characters and not others, then it becomes a cheat or worse, it exposes those whose thoughts we are not permitted to know. Such an incongruity leads to distrust and the ending will feel slightly dishonest.

Those are my thoughts. Do you agree?