They could, but the primary limiting factor of maneuverability is the integrity of the airframe, not the human inside.
I doubt it's a fundamental limitation of materials or physics, just of the constraints given to the designers of the aircraft.
You can over-G an F-16 at 4G depending on airspeed and loadout. That's well below (trained) human tolerances.
Sure, you can build a drone that can handle 1000 cycles of 16G turns, but it's likely not going to be cheap, repairable, fast, capable of carrying weaponry, etc.
Limit loads are the design point, which are 1.5x lower than the ultimate loads, which are still lower on actual aircraft than what humans can handle (and are not meant for sustained or repeated operation).