The Zumwalt was designed to replace the Ticonderoga class cruiser. The high cost is the result of ill-defined mission parameters as defined by both the senators and congresspeople at first wanting a replacement (which is what the navy needs), then a BMD platform demanded by these elected officials onto the admirals (who consequently need sponsorship for promotion). That means that mid-build, the entire ship had to be redesigned for BMD, which added significant costs to this model. Add snowball effect, and the current Zumwalt iteration is overbudget and mission-wise has much less offensive power than the proposed original design.
It will still perform very well, but the 3 ships of the class are technology demonstrators used to gain knowledge on new propulsion tech, tumblehome shape, and a much more powerful radar system. The U.S. Navy will use this knowledge to build their future fleets of Burkes or Ticonderoga replacements, just as they used the Seawolf submarines as a demonstrator for the Virginia-class.
Frankly, because of the size and firepower, I can't tell if it is a cruiser, destroyer, battlecruiser, or battleship (due to the two 155-mm cannons).;D