So why can a thrust vector control system increase my maximum g-load capacity? Because still n=L/G is relevant and if I can not provide enough lift (pointing up) to counter balance the thrust (pointing down to spin a missile around c.g.), why should I use it?
The point of thrust vector control is post-stall maneuvering.
Control surfaces lose much of their effectiveness when the flow over them is separated. Pointing the jet exhaust in different directions works almost regardless of angle of attack. All that is required is good intake flow, and by placing the intake below the forebody (as done on the X-31, the F-16 or the EF-2000), this is still possible even at high angles of attack.
Post-stall maneuvering enables the airplane to point its sensors and weapons in the direction of an opponent within seconds of detection. Compare that to flying a turn at Mach 0.8 over maybe 150°. At 6g (= 80° bank angle), this takes 11.5 seconds, assuming a speed of 256 m/s (which is Mach 0.8 at medium altitude) and an instantly achieved maximum turn rate.
By attaining a very high angle of attack in order to slow down the airplane and thrust vector controlled rotation of the fuselage into the direction of the opponent (Herbst maneuver), an airplane can turn much quicker and, consequently, shoot earlier. This is critical for winning in air-to-air combat.
A max G limit is generally imposed due to the load the wing is capable of. Specifically, the bending moment it can sustain.
Think about it, in a hard turn the wing and fuselage experience forces in opposite directions: The wing is creating lift in the direction of the turn, while "centrifugal force" wants to sling the fuselage to the outside of the turn. This makes the wing bend.
However, in the same turn if you had a thrust nozzle that could generate thrust acting on the fuselage towards the inside of the turn you would reduce that bending stress on the wing, increasing the margin for G available.
ADDENDUM: While I think my explanation is useful, (based on my interpretation of the question) it is highly unlikely that a VTOL type jet would use this technique at high speed to counter the risk of structural overstress. Rather, aircraft like the Harrier can use this to its advantage when maneuvering at lower speeds to reduce the risk of an accelerated stall.