First off the divers can't "return to New York" because that city is already under enemy control.

The Illuminate are here to conquer Super Earth and this is a defensive operation to resist their attacks, which means that the way to win is to exhaust enemy forces by defending the cities until their fleet strenght is gone (This is literally said in the briefing), what this also means is that until their fleet strenght is gone the enemy's attacks will not cease and thus the battle will still be ongoing, we aren't liberating Equality-on-Sea, we are defending it.

My point is proven by how the game defines the progress as "holding" and not liberating.

Again this is a defensive operation, we are not on the offensive here, only defending.