I thought the Zumwalts had an altered primary mission now, mainly anit ship. It is my understanding that the littoral mission had been dropped a while ago.
My view already partially covered by above posts, the Zumwalt destroyers were designed and built to replace the Iowa battleships for land bombardment to support the Marines. The impression was the Navy was not too enthusiastic on taking on this mission, reducing Zumwalt buy from 32 to 3 ships, even tried to cancel 3rd ship but overruled by Pentagon. Navy cancelled the LM LRLAP, the GPS long range land attack projectile rocket when costs escalated to $800+thou per round and it could not reach specified range. The LRLAP ammo for Zumwalts is the only munition able to be fired from its two huge AGS 155 mm guns and fit the automated magazines and handling system.
Navy was left with three $8 billion white elephants and following year Dec 2017 came up with a new mission for Zumwalt, an"offensive surface strike platform" using its 80 VLS cells for the Maritime Strike Tomahawk V with its new seeker to engage moving target at sea, has been mention of using SM-6 in anti-ship role, question whether Zumwalts SPY-3 radar has ability to use SM-6 in AAM role. The Ticos and Burkes can carry out the Zumwalt "offensive surface strike platform" role as well as using their Aegis for AAM and BMD, so in effect its a made up role to justify the continued existence for the 3 Zumwalts with their oddball radar, sonar, CMS etc.