More travelers are shelling out for the best airplane seats amid a boom in premium travel, driving airlines to develop increasingly complex business-class seats — some of which are proving to be a headache for carriers and manufacturers alike.

Since COVID-19, airlines have been packing their planes with fancy new cabins as they try to attract more deep-pocketed customers. In April, United Airlines rolled out an airplane with 64 business-class seats. Delta Air Lines plans to debut its Airbus A350-1000 next year with 53 business-class suites.

But new seat designs must undergo rigorous certification by aviation regulators. And ongoing approval…