Etihad Airways, the national airline of the United Arab Emirates, already has among the most lavish first-class cabins in the business, and it’s about to step up its game another notch. The airline will soon take delivery of ten double-decker Airbus A380s with a new twist: in addition to the usual luxurious first class service, passengers will be able to book “The Residence,” an immaculately outfitted three-room suite, featuring a chilled minibar stocked with fine wines, a dedicated bathroom with a shower—and best of all, trained butlers serving chef-cooked gourmet meals. It’s the kind of luxury one would expect only...