HO CHI MINH CITY, Vietnam—With the U.S. and China tangled in a nasty trade fight, this should be Vietnam’s time to shine. Instead, it is becoming increasingly clear that it will be years, if ever, before this Southeast Asian nation and other aspiring manufacturing destinations are ready to replace China as the world’s factory floor.

The specialized supply chains that made China a production powerhouse for smartphones and aluminum ladders and vacuum cleaners and dining tables are nowhere near as developed in Vietnam. Factories...