I wouldn't be surprised if the carriers didn't carry missiles. Making a jack-of-all-trades ship that can do everything is not efficient (that's presumably why we see most of the ships are specialized ships like cruisers and carriers and lighter escorts; only a very few are "do everything" ships like the Concordia or the Gettysburg (supercruiser) ). I mean, you could stick missile tubes or anti matter guns on a Snakeir or a Hakaga, I'm sure, but the space you take up to do that would eat up some of your capacity for fuel storage, magazine, damage control, a few extra bombers, etc. And frankly, a carrier doesn't really need missiles -- it has lots of bombers that can attack other cap ships or bombard planets from much greater ranges than missiles can.
(Regarding jack-of-all-trades ships, we do see hangars stuck on cruisers and destroyers because, in the fighter dominated world of WC, it would be suicide not to. Any ship without any kind of fighter capacity would be completely unable to operate in any area without carrier support).
If you're going to arm some of your ships with anti-planet missiles, it makes sense to arm your fastest ships with missiles: hence cruisers. These can maneuver around away from the main fleet and strike with them, exactly as occurs in Fleet Action. In fact, this is not too dissimilar from the manner in which frigates were used in the 18th century. They weren't your main ships of the line, but because of their speed and maneuverability, they would maneuver away from the big fleets to take out the commerce and supporting ships.