TVC is without a doubt designed with greater agility in mind, but it brought also other benefits...
Russians realized while developing the TVC versions of the proven AL-31F family, that when flying at low level, the engine gave more stability and controllability for the pilot. And this of course made the plane safer/easier to fly at low level....TVC engines gives the pilot very good control of the plane at slow speed flight and especially during/after stalling the plane (see some of the Su-37/30 videos), thus making it a safety issue....If you remember the Su-30MK prototype's crash in Lebourget air show in 1999, (or see a movie clip of the accident on youtube.com) one thing that saved the lives of the two pilots was the TVC...Averyanov (the pilot) was able to pull the Su's nose over the horizon, and thus making it possible to gain a little bit of height to eject...
...But yes, TVC gives the pilot unparallelled and 'unrestricted' controllability of the plane, making it possible to 'swing' the plane like it has never been possible. And yes, this capability for the pilot, to fly the plane through very (normally) adverse 'moves', gives him/her the edge in a close in, dog fight and knife endge engagements...
Indian Su-30 pilots have also demostrated the TVC's use in BVR fight. They competed against USAF F-15s in a simulated air combat and while the Eagles were closing for radar lock, the Su pilots made some rapid turns to leak the energy and with the use of canard foreplanes and TVC engines 'dropped' below the Eagles radar to force the Eagle pilots to use doppler mode....So, the doppler mode utilises the differense in speed s between an object near ground and the ground itself (which is 0 of course)....Like this, the Su's flew below the Eagles radar near zero speeds, making it almost impossible for the Eagles to make a proper radar lock....Now, the Su pilots were free to use R-27ER/ET missiles in good respects...
There's only two fighters in service at the moment that utilises the TVC capability...The Raptor with 2-D TVC and the Su-30MKI/MKM with 3-D TVC.....