High thrust is required to sustain high G turns as it bleeds off airspeed very quickly. Wing loading, apsect ratio, sweep angle and wing area all have play major parts in the agility of an aircraft. Thrust vectoring and canard foreplanes also help alot usually at low speeds. There is no perfect combination to acheive a certain result.
If the F-22 didn't have thrust vectoring it would probably be the worst when it comes to low speed agility due to its high speed wing design, this is shown by its high landing speed. The F-35 is desigend for slower speeds though still quick which means it doesn't require thrust vectoring. Thrust vectoring also adds weight and reduces the thrust to weight ratio, so thrust vectoring could reduce sustained turn rate instead of improve it.
The turning part is not entirely correct. High G turns not necessarily rely only on high thrust. It happened when the aircraft is changing its direction rapidly, and all aerodynamic devices had to cooperate and well, in order to achieve such a maneuver. It is true that there is a ratio of lost in thrust in the process of directing it away from the axis of the engine, however, an co-axis thrust assist the airframe to maintain a high centripetal force, in other word a high G condition, but the tangential force from a co-axis thrust also laying much more pressure on to the lift devices which is inverse proportion to the radius of turn, while VT is a solution to bypass such a circumstances. VT achieve a small radius turn by changing the position of the longitudinal axis closer to and ideally on the barycenter of the airframe, in oppose to force the airframe to turn near a given axis. As a turning rigid body, regardless of method of turn, it creates G force proportion to the rate of turn.
Take note that the lost of thrust also happen on a co-axis thrust which act as a tangential force in the turn. When the airframe is well on the direction of flight, the nozzle rotate back to its position, lost of thrust no longer happen. Due to such a complex and precise mechanism control, thereby a digital flight control is a must as oppose to a conventional thrust design.
The so-call lost of KE in a VT turn is due to the congenital of the method of turn. When the longitudinal is very close to the barycenter (small radius) and a high turn rate (angular velocity), G force will increase such rapidly that easily exceed the limit, for the airframe as well as the pilot as a human being. To counter such a defect, flight control must maintain a low angular velocity, thereby a limit in low thrust cause a lost of momentum in the engine and the slower regain of KE. As a result, the aerodynamic become worse when there is no thrust to counter the stall effect. On the other hand, co-axis thrust powered aircraft can take a smooth turn upon a longer radius, keeping about the same amount of thrust under the limit of tolerance of the airframe, therefore not much lost of momentum in the engine in compare to a VT engine.
As you can see, there are pros and cons in both systems, but if there is a tech breakthrough to offer more endurance to G force, VT certainly has a brighter future.