I'm hoping to identify an SF story (read it at least 20 years ago, I think), where Earth has set up a base on a distant world, and when the locals see how advanced they are, they quietly give up on themselves, and stop having children.
The governor (or similar) from earth has conversations with the earth military commander, talking about how they really wish they could get earth to leave the natives to themselves, but it won't happen. The military commander thinks the system is broken, but the governor suggests the there are ways to "make the system work for you".
Some time later the governor privately suggests to the commander that maybe teaching the locals about ships and piloting might encourage them to take new interest in life, and the commander requests permission for this from the military.
At some meeting, the governor somehow gets the locals (the locals may be slightly telepathic?) to express interest in some very fragile art form he has one of, which prompts someone to request shipment of many of them as gifts for the natives.
Because they're so fragile, this gets a lot of huge transports ships to the planet, and since meanwhile the natives have learned how to fly, they steal them and emigrate en masse, vanishing into the void.
The military guy accuses the governor of setting this all up (to the reader this is clearly true), but there's no proof, and the story closes with the governor reminding the commander of what he had said about making the system work for you.
What is the name of this story?