Despite the DDG designation, the Zumwalt is a capital ship.
You're right. For comparison everyone, consider:
The WWII era Fletcher class destroyer was a light, fast 2500 ton or so. The modern flight III Arleigh Burke DDGs are (IMHO) a bit big for a destroyer designation at 9800 tons. (light cruiser anyone?) That's about the same as the Ticonderoga class CGs. Admittedly the Ticonderoga class CGs are just a bulked-up Spruance class DDs which were 8000 ton or so. The old Virgina class CGN - nuclear powered guided missile cruisers - were 11,600 ton.
So yeah, the Zumwalt DDGs at 14,500 are seriously stretching the notion of what a destroyer is. If you're going to call the Ticonderoga and Virgina cruisers then based on size, capability, and planned numbers you really should call the Zumwalt a cruiser or even a heavy cruiser. (ie a CG not DDG)
The Zumwalts really should have rec’d the CG (or even CA) designation. The Ticonderogas aren’t really cruisers, being built on Sprucan destroyer hulls, and when they’re gone the Cruiser designation will pass out of use in the USN.
And yes, I know that the intent was to build a Ticonderoga replacement CG using a modified Zumwalt hull. But that was dropped over 10 years ago ... so I guess we’ll see a LOT more O6’s driving Destroyers rather than O5’s.
For decades, the Navy has been getting around the budget planners by calling cruisers, "destroyers". A typical WW2 destroyer like the USS Doyle was 348 feet long and weighed 1,630 tones. Then again, WW2 capital ships had bigger crews (Chicago had 1,142 officers and enlisted). The Zumwalt has fewer crew than the USS Doyle (Zumwalt 142, Doyle 272), so by that standard of measurement Zumwalt is more like a WW2 frigate.