Thanks for your input Ray and Virtuali,
This is very interesting, I disabled all sceneries in the Scenery Library menu except for those which simply cannot be disabled (greyed out). It's important to note that this is a fresh P3D install, and I also made sure to manually delete any "leftover" files in Documents, Program Files, ProgramData, and %APPDATA% before reinstalling. So there should be no addon scenery present.
Interestingly, this leaves only two airports in the P3D world: NZCI (Chatham Island, New Zealand) and NTAM (Rimatara, French Polynesia).
Upon load, I saw a message that the airport cache was regenerated in 4 seconds. Then GSX & Couatl close without prompt again. On further loads I see a message that the airport cache was successfully loaded, then the same issue. In this case, the issue must be aside from the airport cache generation. Really odd.