I think the main problem is the gas-turbines. With the navy already planning railguns and lasers for the Ford class carriers (hence the hugantic reactors) I can't see the Zumwalts having much of a future. Instead I think a lot of the knowledge gained during their designs will be passed onto a future cruiser-class vessel. This future ship will see guided missles cruisers and destroyers blend together (the Zumwalt is already dramatically larger than a Ticonderoga class cruiser).
In the future, we will likely see a new fleet of cruisers built that combine DDG and CG classes together. These ships will likely weigh in around 25k tons and some of the former roles of destroyers will fall to littoral combat ships. All to accommodate a nuclear reactor.