No, the USN genuinely think of zumwalts as destroyers. There was a separate project to design a cruiser counterpart to the zumwalts. The cruiser didn't have zumwalt's tumblehome hull, and was designed for blue water fleet air defence. It was cancelled when future air threat to the fleet was underestimated while cost of Iraq war escalated.
The CGX program was specifically designed to replace the Tico with a future guided missile cruiser combatant principally geared towards air defense.
My guess is that ultimately there will be a cruiser replacement. It may well end up being for the next 20 years to be the Burke III. But, sooner or later there will be a new purpose built replacement.
I understand full well that the Zumwalts are "officially" classed destroyers. I have been involved with and following these process for over 30 years now. And that is fine. People can call things whatever they decide, for whatever reasons, particularly the Navy and Government people who get to make the official designations.
However, none of that changes the fact that with their displacement, with their heavy direct fire capability, with their heavy ground strike or surface strike guided missile capability, they are what would be traditionally known as cruisers...and cruisers which are also extremely capable in the air defense and ASW roles as well.
There has been a lot of talk for several years at the US Naval Institute about this and the "unofficial" consensus is that they are in fact cruiser type vessels that the US Navy and US government has decided to call destroyers.
But all of this talk about the Zumwalt is really off topic here on the PLAN Type 055 thread and should be moved over to the Zumwalt thread itself.