I'm answering because I think there is an aspect of the use of magic in the LoTR that I commonly see ignored and is ignored in many of the answers.
tldr;
One does not simply fly directly into the gaze of the Lidless Eye.
Long Version
Enchantment vs. Magic
I am not a <PERSON> expert, but my understanding of <PERSON>'s use of magic, I believe described in his "On Fairy Stories", distinguishes between a more mechanical kind of magic and a more spiritual "enchantment". Forgive/Correct me if I'm misusing his use of the words. It's been a long while since I've read it. There are many many examples of this enchantment, but some that spring to my mind are <PERSON>'s description of the character of staves that he gives to <PERSON> and <PERSON>, and of their experiences with the elven cloaks, roap, boats, etc. No concrete rules of physics are established. Instead, objects seem to vaguely bend the rules of physics in accordance with the atmosphere/nature of the object or their creator. And it's often not completely explained or even explicitly claimed. It is noteworthy that we're never conclusively told whether <PERSON>'s rope untied itself at his call or whether his knot was bad when they climb down the cliff at night. When the party is climbing Caradhras, they discuss whether the "fell voices" they hear are the wind or some creature. <PERSON> likes to maintain uncertainty, and it's more about the mood & (spiritual?) atmosphere than the physics of what is occurring. Another example is the way the book describes the wills of <PERSON> and the <PERSON> when they first confront one another on each side of a door, although that is a little more explicit. Also, when the 3 travelers <PERSON>, <PERSON>, and <PERSON> are chasing the orcs who have captured <PERSON> and <PERSON>, they talk of a hostile will that is set against them as they journey that is making their trek more wearying. <PERSON> doesn't usually enumerate the way the different people and objects can manipulate the laws of physics like some other fantasy works of literature (in contrast to the use of the One Power in the Wheel of Time, for example). 88
Instead, <PERSON> creates "atmospheres" and "auras", for lack of a better word, around people and objects to give them a sort of personality, a nature, a character. It's part of what makes the conflict between good and evil so epic in the story, I think. <PERSON>'s use of wizardry and sorcery in LoTR is, in my opinion, more along the lines of "enchantment" (as referenced in "On Fairy Stories"), but I consistently see people treating it as a mechanical manipulation of physics. <PERSON> is an interesting example, as we can name some specific mechanical feats he can accomplish with fire. But other things he does are more vague and more about who he is than any ability we could name. His power as compared in the story in the eyes of <PERSON> with <PERSON>, for example. (This is also why doing things like pitting <PERSON> against Darth <PERSON> in a fight don't work well, in my opinion. You have to decide which kind of magic/powers the fight will be composed of, and in my opinion, that determines who will win.) <PERSON> is the same way, as is <PERSON>, <PERSON>, and most of the characters in the book.
<PERSON>'s Power is Firstly Enchantment, not Magic
One of the objections I saw raised to the eagle plan was that <PERSON> could conceivably throw fireballs at <PERSON> on an eagle, but I think this misses the point of <PERSON>'s power. There is one part of the story where <PERSON> says somewhat ominously that he has not yet been tested against <PERSON>. And <PERSON> when he confronts <PERSON> with the <PERSON> barely has the strength to overcome him and wrest the stone away. It is mentioned that if the hobbits were captured, there is no doubt that in the end they would tell everything. And I don't think it would be in line with <PERSON> to attribute this to merely physical torture. See <PERSON>'s encounter with <PERSON> through the stone. I think you could attribute parts of this to some mechanical ability, but not all of it.
This is one of the beautiful things about <PERSON>'s writing that the movies could not or did not fully convey, I don't think. 300