Actually, Zerosnark, while the role of the CG and DDG in the current US navy might be the same and the armament very similar, the volume is quite different. The Bunker Hill sub-type Ticonderoga-class CG can actually put a greater volume of missiles, be they BGM-109s TLAMS, or SMII SAMs into the air than the Arleigh Burke or Spruance. Ticos just have a greater number of VLS cells with which to hold weapons.
It is no longer the the size, but the capabilities that the vessel brings to the table and where those capabilities fall when compared to other ship classes (of the same time period) that is used to classify ships. That's why the Ticonderoga, though at a similar displacement to the Spruance (and indeed based on the Spruance hull) is considered a CG. The average capabilities of a Naval vessel have increased greatly since 1950, which is why the Tico isn't a BBG (if there were such a thing).
I don't think I've ever seen a long-serving ship "demoted" in designation, save for the Essex, but that's partially because usage was changed. Yet there are several starships in the Trek universe that underwent designation changes. The Miranda was initially a heavy cruiser and in the TNG era it's a destroyer. The Excelsior was a BC, and now it is down to a CA. It's because comparable capability has been decreased in the face of the Galaxy, Nebula, and Akira. Can you imagine the day when the Akira is considered a CL? I would not want to stand toe to toe against whatever is heavier!
I think the World War II classification system works better for Star Trek than the newer system, simply because I don't think there would be such a thing as a DDG or CG by the TOS era, as missiles had been replaced by photon torpedos for at least forty years. It still isn't perfect. I think this particular system uses a combination of comparative striking power, displacement, armor, and in a great part role to determine designation. For instance, you wouldn't find a a Destroyer on the line of battle or a Battlecruiser escorting a convoy during Worl War II, and yet these circumstances are pretty common in the Trek universe.