actually, CVs are not unsinkable, well, at least one of them was sinkable. Saturday night we sunk an American CV using the guns of C3 and PT torpedos.
However, there is the issue of the other ships respawning out in the ocean instead of waiting for the whole fleet to respawn at the port. So the fleets should remain out of play for that reason, as well as some CVs may in fact be invulnerable.