Last year, a company called Flytenow was poised to revolutionize air travel by allowing private pilots already going to a destination to share their costs with would-be travelers—kind of like a college rideshare bulletin board, but on the Internet. The service would pair pilots with potential passengers, for a small fee no greater than the cost of fuel. It’s been called “Uber in the sky.” But in December, Flytenow shut down after the U.S. Court of Appeals for the D.C. Circuit upheld the Federal Aviation Administration’s determination that the service must obtain the highest levels of licensing, akin to what...