Take out the "heavily contested" part, and you can make a case for it in numerous cases. Korea, Lebannon, Grenada, Panama, Gulf War I (where it was used as a feint), etc.
Of course, that does not mean in the future it will not be heavily contested. The US was not really prepared for World War II in this regard, and had to build the capability up. In any major Pacific or even Mediteranean war, or European...no doubt it could happen again.
Right, but the current global strategy of the US leaves less and less room for marine expeditionary missions. Put more simply, there's less of a need to land on beaches against nations with substantial anti-shipping missiles now.
The only case in which I could see the Zumwalt being useful would be a knife fight in the close confines of the Persian Gulf, where the Iranians could employ short-range radars and AShMs to risk USN assets. But otherwise, the Zumwalt is a case of overspending, I think. If the USN wants to make a ship stealthy, it should focus on the large ships who would be the natural targets of long-range weapons, like AAWs and carriers.