Why do the drones need to be controlled by a pilot who's already flying an aircraft? Couldn't a drone sensor platform perform the same task with remote operators?
Another might be latency, if under active control. I imagine the purpose of the F-35 as a drone platform is less about active control and more about being a coordinator node though.
This is precisely why. Iran has shown that it can, on some level, interfere with long-range communications of drones. I'm sure the Chinese have even more such capability. Having a C&C platform within the same battlespace limits communication exposure.