An aircraft will become less recoverable as the CG moves aft. Realize there are a lot of other factors as well, but the deal is that a more forward CG makes the plane more recoverable, but the tradeoff is that you have to have the tail surfaces create more balancing force down to keep the plane in level flight - which creates more drag. So I could have 2 identical aircraft, and a CG placement just a few inches forward on one will make the AoA on the wing and the trim settings totally different to make it cruise level. Moving the CG a few inches aft makes the same aircraft cruise a bit faster, but the tradeoff there is that if the CG gets too far back then the plane tends towards getting into a flat spin (unrecoverable).
This is why you see aircraft burning off fuel tanks in a particular order - the CG changes as the fuel is burned off and the plane will handle differently. In the P-51 it was necessary to burn off the tank behind the pilot first to keep directional stability by moving the CG forward. You could fly it straight and level with the tank full, but if you pulled any wild maneuvers with that weight back there you were taking a risk. There are a couple of stories out there about pilots who burned the tanks off in the wrong order and managed to get home to tell the tale (maybe it was Yeager?).
Anyway - realize the whole thing is a balancing act between forces (thrust, lift, drag, control surfaces), requirements (payload, range), and performance. You want your fighter aircraft to be on the ragged edge of stability / instability because you win if your ride does something that the other guys ride can't do. I give a big <S> to the guys that flew those planes, but I also have the utmost respect for the guys that were designing them on paper and doing the math with a slide rule.