North Korea and Iran are not in the same league as China and Russia. The first two use mainly very old, not very advanced systems, the latter have very advanced systems. In case of China, there is also the economical and industrial base to develop the navy even further. China appeared to have passed the point, where it was dependent on imports and copying. Russia is dependent on imports of technologies and its naval modernization programs suffered massively from the embargo after 2014 (e.g., Ukraine had built most gas turbines for Russia, many Diesel engines were German - both were not delivered after 2014). North Korea and Iran lack the access to modern technologies and do not have any strong economical and industrial base, especially North Korea.
Compared to the LCS, the Zumwalt class is very different. As designed, they would haven been very sophisticated, well equipped and advanced ships designed as first class fighting ships, to be better than anything comparable. The resulting ships are still very good, but suffer from not getting half of its radar (the SPY-4 antenna) and some other parts of the planed equipment. Most famous is the lacking 155 mm ammunition, but many people ignore that these are only part of the secondary armament. The VLS MK 57 was always the main armament. If the class will get a proper radar - which was already announced - they will be superior to the older 1970s and 1980s designs in service with the USN. Any new DDG/CG design can be developed from the Zumwalt.