We went with AIR mainly because we do most of our development/debugging/testing in the Flash target. If it runs in the Flash player, it pretty much runs the same way in AIR across the supported platforms.
We also wanted the rendering to be the same across our web and desktop builds. There were some incompatibilities between the Flash and native targets in Lime 0.9.7. For instance, the BlendMode.OVERLAY blending mode didn't work in native builds, so we had to settle for a less pretty hack there. Also, tabs (\t) didn't work for aligning text in the native builds.
I think Adobe AIR does a great job at providing an environment to interact with the OS. We made use of Flash/AIR's file open/save dialogs for debugging purposes. You can get those in the latest Lime/OpenFL, I think, or through the systools haxelib, but that's one more dependency in your project.
A lot of things come working right out of the box with Flash/AIR. Of course, in order to maintain parity in our Linux build, we had to use other libraries or write our own solutions. If you're only targeting Windows, OS X, or maybe even Android and iOS, I think wrapping in AIR is a viable solution.
We would have gone with AIR for the Mac build as well, but something in the FRESteamWorks native extension for Mac didn't work. I'll have to investigate that further.