The naval terminology reflects a displacement class and use case, not a specific design.

The now-cancelled DDG(X) next-generation destroyer already had a larger displacement than a heavy cruiser. And it was cancelled for not being large enough to support its mission load-out as a modern destroyer.

The name “battleship” may be archaic but the displacement requirements for the next-generation destroyers (or whatever they are eventually called) are roughly in “light battleship” territory.

To put it another way, we were calling battleship-class ships “destroyers” for historical continuity reasons. Over time, ships in a class have become much larger but we kept the old names. Even the older Arleigh-Burke destroyers would be traditionally classified as heavy cruisers if they were commanded by a flag officer.