I'm leaning towards the idea that building a ship such as Popeye has proposed would be a good idea. It won't be the best surface warship necessarily, but that doesn't matter. You learn by doing, and learn from your mistakes. The Chinese know the principles of warship construction, nuclear propulsion, how to build large ships and much else besides. Bringing all this expertise together in a single shipbuilding project like this would be of enormous benefit to the Chinese, and will open up the possibilities for the successful completion of other major projects. For example, lessons learned from the design of the underwater hull and subdivision/watertight compartments will translate relatively easily to a larger hulled warship likea carrier than simply scaling up from a frigate or destroyer design.
Historical parallell, in 1905 nobody had ever built an 'all big gun' battleship, but that didn't stop Jackie Fisher from going ahead. In a year and a day Dreadnought entered service and the rest of the world's fleets became obsolete overnight. Mistakes were made (eg putting the forefunnel in front of the fore mast so that the spotting top was uninhabitable when underway) but the lessons were learned and following ships were improved steadily and empirically. For all Dreadnought's faults, and remember she herself had become obsolete by WW1, she was worth the effort, and I believe the hypothetical chinese battlecruiser would also be worth the effort, even if only for the learning experience.
Historical parallell, in 1905 nobody had ever built an 'all big gun' battleship, but that didn't stop Jackie Fisher from going ahead. In a year and a day Dreadnought entered service and the rest of the world's fleets became obsolete overnight. Mistakes were made (eg putting the forefunnel in front of the fore mast so that the spotting top was uninhabitable when underway) but the lessons were learned and following ships were improved steadily and empirically. For all Dreadnought's faults, and remember she herself had become obsolete by WW1, she was worth the effort, and I believe the hypothetical chinese battlecruiser would also be worth the effort, even if only for the learning experience.