“Do I need their permission to fly a kite? An RC plane? A hobby rocket?”
Actually, you do, if it’s in certain areas, or over certain altitudes.
BATF is the primary controller of Model Rocketry, for example.
Intercontinental Beer Missiles -- there's an answer waiting for a question --
BATF might regulate the solid fuel “engines” since those are technically explosives. But they don’t control what I can shoot into the air, do they? And again, under what authority?