U.S. airlines retooled their businesses over the past decade in ways they said would generate profits even during an economic shock. The coronavirus epidemic rippling around the world is providing the biggest test yet of those efforts, grounding hundreds of jets overseas as consumers and businesses scrap travel plans.

The most significant operational impact for U.S. carriers has been mass cancellations into April of flights to and from Asia. American Airlines Group Inc. and Delta Air Lines Inc. suspended flights to Milan...