Ignoring why the Borg would require a mouth piece for a second. Had the Borg Queen truly been nothing more than a mouth piece (like Locutus was), I would not have been as annoyed at the concept. But the Queen we see is obviously much more than a mouth piece. She was looking for a partner basically to help her rule the Collective. Gone was the will of the Collective and it was replaced by the will of the Borg Queen.
As a result of having the Queen, the Borg lost their singular collective mind of "You will be assimilated. Resistance is futile
" and replaced it with "You will be assimilated. After the Queen gets what she wants, and when we get around to it.
Think about it, don't you think the Borg could have easily overwhelm the crew and assimilate all of E-E if the Queen had not been hell bent on finding a mate? Yes, I understand that you can't make a villain that our heroes can't destroy. But I would have liked it a lot better had Picard actually blown up E-E to destroy the Borg, and either show they somehow rigging a Deus-Ex-Machina temporal device to get home, or have the temporal police come and pick them up.
Though if that had happened, there is no way the Vulcan sensors wouldn't pick up the explosion. damn... there sure are a lot of annoying parts in the TNG movies.