To add,
Glorfindel I (GI) might contain an easier reason: that Glorfindel was a companion to Gandalf on his voyage to Middle-earth in the Third Age, possibly as a guard or assistant in addition to being a friend and follower (considering the first words of the second page anyway, noting that the first page is missing).
Quote:
'... as guards or assistants. An Elf who had once known Middle-earth and had fought in the long wars against Melkor would be an eminently suitable companion for Gandalf. We could then reasonably suppose that Glorfindel (possibly as one of a small party, more probably as a sole companion) landed with Gandalf-Olórin about Third Age 1000.'
[skipping to end of GI]
'(...) It is indeed probable that he had in Valinor already become a friend and follower of Olórin, Even in the brief glimpses of him given in The Lord of the Rings he appears as specially concerned with Gandalf, and was one (the most powerful it would seem) of those sent out from Rivendell when the disquieting news reached Elrond that Gandalf had never reappeared to guide or protect the Ring-bearer.'
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Tolkien seems to reject this in
Glorfindel II, but there he appears to be considering it an improbable exception that Glorfindel be sent to Middle-earth after the Blessed Realm was removed from the Circles of the World. OK, but as the focus of the trip was really Gandalf and the mission of the Istari anyway, I don't think it necessarily would make Glorfindel
'... of greater power and importance than seems fitting' (GII) to have him accompany the Wizard.
Hmmm. I kind of like this explanation from GI myself.