For one:
At the stage Glorfindel came into the story Tolkien himself was unaware of how much gloomier things will turn out towards the end
For two:
Glorfindel was way too perceptible.
Cf:
Quote:
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With his last failing senses Frodo heard cries, and it seemed to him that he saw, beyond the Riders that hesitated on the shore, a shining figure of white light; and behind it ran small shadowy forms waving flames, that flared red in the grey mist that was falling over the world.
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also:
Quote:
'I thought that I saw a white figure that shone and did not grow dim like the others. Was that Glorfindel then?'
'Yes, you saw him for a moment as he is upon the other side: one of the mighty of the Firstborn. He is an Elf-lord of a house of princes. Indeed there is a power in Rivendell to withstand the might of Mordor, for a while: and elsewhere other powers still dwell.
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It would not have been easy for him to use stealth. Apart from Ringwraiths, who surely would have seen him as he was 'upon the other side', Silent Watchers would have wailed at his approach, I believe
And the second half of the quote (Indeed there is a power...) would serve as reason number three:
For three:
Someone should have been left behind to 'withstand might of Mordor' in case of direct attack (which was attempted too, mind you)
***
For general reincarnation purposes:
here. Not directly related, but touches upon some aspects. There are other interesting threads about it, I'll try to provide the links when free for the endevour.
cheers