Note: Thisis strictly a personal opinion, no real scholarship should be derived from this response.
I believe that having
Glorfindel deliver
Frodo to Mt Doom would be a tragic mistake, doomed to almost certain failure.
The primary objective of the Fellowship was to destroy
the Ring by taking it to the fires of Mt Doom by stealth. I find it hard to accept that an Elvin Prince, even of such power as Glorfindel possessed, could slip into
Mordor undetected.
Also, we have no direct evidence that the
Elves even knew of
Shelob's lair existance, let alone a working knowlidge of how to navigate through the labyrinthine passages. This leaves only three possible means of entering the Black Land.
By passing the
Black gate by force
By passing, either undetected or undefeated, through the
Morgul Vale
or
by escorting the fellowship through the back door by either circumnavigating the
mountains and transversing the wastelands to the far south or far east.
The first two of these alteratives seems to me to be only possible by a large, highly mobile fighting force, which neither the Elves or
Gondor maintained the resources to provide. The third choice would require a considerable greater expense of time and a vastly more provisioned means of
travel for the Fellowship: thereby negating the only small advantages the Fellowship possessed. Namely Stealth and Speed.
A third reason for not having Glorfindel as a member of the Fellowship is that I doubt very seriously that
Elrond considered sending him in the first place. Remember that
Sauron waged war on a great deal more territory than is shown in the text. It is only after the defeat of the
Dark Lord and the destruction of
Barad Dur that
Gandalf gives the account of the war in the North.
If the quest to destroy the Ring had failed and Sauron had regained the fullness of his native power, the Elves would be forced to fight their way to the Havens. the Power and Majesty of Glorfindel would have been much better served by holding the last means of escape open for the final flight than marching to war in the south.
Just my thoughts on the matter
feel free to disagree
RD