That's why many (most, all?) surface to air and anti-air missile systems are designed to pull big G loads. (numbers I've seen are roughly 3x max pilot tolerance) That way there is just about no possible way a piloted aircraft can turn inside them and evade. An RPA could enjoy a similar advantage, if you could get the "scene" back to the pilot with little or no latency, and provide a complete enough picture for dogfighting level situational awareness.
Also, another part of the G load limit on current airframes is simply due to service life limitations. The more and the harder you stress the airframe, the sooner it gets de-certified for flight due to metal fatigue. Though the several fighter pilots I know or have know are the kind of guys that aren't going to let a number on a gauge stop them from doing whatever it takes to win an engagement...
What happens when someone interrupts the wireless signal between pilot and machine? Iran managed to hack a US drone and bring it in...