IMHO, the major problem with drones is a next hell layer of micromanagement:
Usually, my spaceyards are building ships while rest of the planets build units. Drones are rather expensive and hence the build rate is slow. To fill the drone carrier I must move it all around the system picking odd drones here and there. It is much, much more easier with fighters, which can be launched, moved to the pick-up point and recovered by carriers. Drones can not be recovered.
Regardless of their effectiveness, I practically abandom drones in my most current game. No fun at all.