It appears to have partly about not wanting to risk the more sensitive F-22 on certain missions.
https://theaviationgeekclub.com/one-of-the-f-117s-secretly-deployed-to-the-middle-east-to-take-part-in-oir-made-emergency-landing-in-kuwait-scramble-magazine-says/“Scramble editorial note: The owner of the iPhone is trustful. Unfortunately, he was not allowed to give us the pictures of AAS as scrupulous rules were given to all AAS and OIR personnel about the emergency landing at that time. (but we can assure you, although of poor quality, they looked adrenaline-kicking great!). Following the F-117s flights through Death Valley, the involved person consulted a high ranking OIR commander who gave permission to publish the aforementioned words.”