That's true, but then that still doesn't seem odd to me. If there's supposed to be a Composer keyed for specific Halos, then having the Index be a command key for it, either directly or through the control center, make sense.

That said, I didn't really get the impression from Halo 4 or Silentium that the Composers should have any reason to be "anchored" to any specific installation, unless the Didact is essentially resurrecting deployment plans for the Composers that were either considered or abandoned before his time, or that he was starting to put into place before the Librarian stopped him—maybe even using the Halos as mobile Composers.