Why would Glorfindel or another high elf draw Mordor's attention but the Istari don't?

Question

Elrond proclaims that if he had the elves of old at his disposal, that it would do nothing but arouse the power of Mordor. Gandalf seems to claim the same thing about Glorfindel (will find the quote soon, hopefully), which comes to my point: why would a high elf (or Glorfindel, who could apparently veil his power like an Istari) arouse Sauron and a wizard wouldn't.

Is there any explanation in the books for this?

Answer 1

Elrond says:

"The number must be few, since your hope is in speed and secrecy. Had I a host of Elves in armour of the Elder Days, it would avail you little, except arouse the power of Mordor.

The Company of the Ring shall be Nine;"

So Elrond is merely saying that it's not a good idea to send many people, and certainly not an armed battalion.

Also Gandalf says when pondering the inclusion of Merry and Pippin making up the last 2 spots in the company:

"I think, Elrond, that in this matter it would be well to trust rather to their friendship than to great wisdom. Even if you chose for us an elf-lord, such as Glorfindel, he could not storm the Dark Tower, nor open the road to the Fire by the power that is in him."

So Gandalf doesn't say Glorfindel would be too easy to spot, he is merely saying that he prefers Merry and Pippin in the company because of their friendship with Frodo; and because the only benefit of Glorfindel (his power) wouldn't be nearly enough for the task.

Answer 2

While this is speculation, I can come up with two plausible theories.

1. The Elves of old were actually more powerful than the Istari. Several of the old time Elves took on multiple Balrogs, and slew dragons much more powerful than Smaug, both of whom caused Gandalf 'some trouble'. Remember that the Istari were not sent with the intention of using their power to defeat Sauron, but to aid and guide the inhabitants of Middle-earth. They may have been deliberately sent with less power than a Maia might be capable of.
2. The Istari were better at 'veiling their power' than the Elves. As above, since they were supposed to be not using their power openly, that would make sense. Not attracting attention was one of the reasons they were sent.

Of it could be both of the above.

Answer 3

An Istar is less powerful than a High Elf

After their arrival in Rivendell, Gandalf tells Frodo that High Elves like Glorfindel are powerful beings and that they are a part of the "real world" and also the "other world".

"Here in Rivendell there still live some of his chief foes: the Elven-wise, lords of the Eldar from beyond the furthest seas. They do not fear the Ringwraiths, for those who have dwelt in the Blessed Realm live at once in both worlds, and against both the Seen and the Unseen they have great power."

— "Many Meetings" (The Lord of the Rings, the Fellowship of the Rings)

One of the mighty Elf-Kings of the First Age, Finrod Felagund, fought a magic battle against Sauron and didn't entirely lose, so Gandalf isn't being hyperbolic here. The most powerful of the elf-lords were able to stand toe-to-toe with a Maia, at least for a short time; and while Finrod was defeated, he was able to stop Sauron from achieving his goal of finding out who Beren and his companions were, or the nature of their quest.

[Sauron] chanted a song of wizardry,
Of piercing, opening, of treachery,
Revealing, uncovering, betraying.
Then sudden Felagund there swaying
Sang in answer a song of staying,
Resisting, battling against power,
Of secrets kept, strength like a tower,
And trust unbroken, freedom, escape;
Of changing and of shifting shape,
Of snares eluded, broken traps,
[...]

Then Sauron stripped from them their disguise, and they stood before him, naked and afraid. But thought their kinds were revealed, Sauron could not discover their names or their purposes.

— "Of Beren and Lúthien" (The Silmarillion, Quenta Silmarillion)

So the High Elves are shown to be immensely powerful beings. But what about the Istari?

After the Battle of the Pelennor Fields, Aragorn visits the Houses of Healing, where he sees Faramir, Éowyn and Merry lying under the influence of the Black Breath. Gandalf is with him, but he says that he wishes that Elrond were there, being the most powerful healer he knows. Later in the chapter, he is joined in healing others of the Black Breath by the Sons of Elrond, but again Gandalf doesn't seem to be involved.

By this time, Gandalf has become the White and been given greater ability to intervene in events, so I feel it is more likely that Gandalf doesn't have the ability, as opposed to not being asked by Aragorn.

Aragorn went first to Faramir, and then to the Lady Éowyn, and last to Merry. When he had looked on the faces of the sick... he sighed. "Here I must put forth all such power and skill as is given to me," he said. "Would that Elrond were here, for he is the eldest of all our race, and has the greater power."

— "The Houses of Healing" (The Lord of the Rings, the Return of the King)

The Istari were Maiar, angelic beings, but their abilities had been diminished. While the Ainur had the ability to present themselves as Elves, or Men, or terrifying embodiments of the sea, or just not at all, the Istari were actually placed into human bodies and thereby cut off from much of their power and abilities.

With the consent of Eru they sent members of their own high order, but clad in the bodies of Men, real and not feigned, but subject to the fears and pains and weariness of earth, able to hunger and thirst and be slain; though because of their noble spirits they did not die.

— "The Istari" (Unfinished Tales)

This was done on purpose, since the Valar had tried to use their majesty and power to lead the Elves in earlier millennia, and it had gone incredibly poorly. So the Istari were placed in the bodies of Men and instructed to hide their origins from those in Middle-earth, to play a supporting role and assist the Elves, Men and Dwarves in resisting Sauron's dominion.

And this the Valar did, desiring to amend the errors of old, especially that they had attempted to guard and seclude the Eldar by their own might and glory fully revealed; whereas now their emissaries were forbidden to reveal themselves in forms of majesty,

— "The Istari" (Unfinished Tales)

It wasn't until after Gandalf's departure that the Elves realised that the the Istari were sent by the Valar for their aid, so it would make sense that they do not shine out like a beacon in the Unseen world. Men, aside from Eärendil, do not survive going to Valinor, and they certainly wouldn't return to Middle-earth afterward if they did.

Even as the first shadows were felt in Mirkwood there appeared in the west of Middle-earth the Istari, whom Men called the Wizards. None knew at that time whence they [came], save Círdan of the Havens, and only to Elrond and Galadriel did he reveal that they came over the Sea. But afterwards it was said among the Elves that they were messengers sent by the Lords of the West

— "Of the Rings of Power and the Third Age" (The Silmarillion)

Answer 4

The passage you're talking about Lexible is when Gandalf disagrees with Elrond and would rather Frodo have his friends go than an elf-lord. He says:

"Even if you chose for us and elf-lord, such as Glorfindel, he could not storm the Dark Tower, nor open the road to the Fire by the power that is in him."

_{The Fellowship of the Ring, Book II, Chapter 3, "The Ring Goes South"}

I believe his point in this passage is that force of arms is not what is going to help get the job done that needs getting done. Besides this Gandalf makes a point to the Fellowship later on how dangerous it is to attempt to enter and leave Sauron's domains.

I alone of you have ever been in the dungeons of the Dark Lord, and only in his older and lesser dwelling in Dol Guldur. those who pass the gates of Barad-dûr do not return.

_{The Fellowship of the Ring, Book II, Chapter 4, "A Journey in the Dark"}