China has spent billions of dollars in recent years trying to catch up to the world’s most advanced semiconductor makers. Two foundry projects, led in part by a little-known entrepreneur then in his 30s, help show why China has yet to succeed. The projects, in the Chinese cities of Wuhan and Jinan, were supposed to churn out semiconductors nearly as complex as the more-sophisticated chips made by industry leaders Taiwan Semiconductor Manufacturing Co. and Samsung Electronics Co., which have decades of chip-building experience. Chinese officials kicked in hundreds of millions of dollars to support the upstarts. But it quickly became...