[Inziladun]

I think the composition of the Nine Walkers, after Frodo, Sam, Gandalf, Boromir, and Aragorn, was largely a product of Elrond's recognition of the "chance" that had brought so many disparate persons to Rivendell at once.
He said during the Council that he had not "called" its members, but that they were intended to find a solution to the problem of the Ring anyway. Seeing that an Elf from Mirkwood and a Lonely Mountain Dwarf were willing and available to go with the Ring, would have seemed too serendipitous to ignore, especially coupled with Gandalf's insight that an elven-lord like Glorfindel would make little difference.