It should be that the J-20 does not have to fly with TVC because its benefits are questionable because of its canard delta design.
Even the British designers don’t agree to the use of TVC in the early Typhoon design.
From Wikipedia,
“the simultaneous West German requirement for a new fighter had led by 1979 to the development of the TKF-90 concept.[10][11] This was a cranked delta wing design with forward canard controls and artificial stability. Although the British Aerospace designers rejected some of its advanced features such as vectoring engine nozzles and vented trailing-edge controls, they agreed with the overall configuration.”
Look what you write is pure fantasy, to start let us see the
compare the wing loading of F-22 and Eurofighter what do you find?
yes you find that F-22 has higher wing loading, despite it has a huge wing actually has worse wing loading than Eurofighter.
I know in your fantasies you expect J-20 to be as light as Eurofighter but
how much does F-16 and F-35 weight at empty weight?
answer is simple F-16 weighs 9 tonnes, F-35 weighs 13 tonnes.
I know you think J-20 has similar numbers to Eurofighter, but not J-20 is at least 5.5 meters bigger than Eurofighter and at least it weighs 9 tonnes more at empty weight.
compare the Thrust to weight ratio of F-22 and Eurofighter what do you find?
well you find that F-22 is in the class of F-15, that actually Eurofighter has higher thrust to weight ratio.
So then why F-22 having the numbers of F-15 is much better than F-15 in maneouvrability, do you want to know the answer?
TVC nozzles and internal weapons bays, yes that is the answer, internal weapons bay that reduce drag and TVC nozzles increase turn rates.
I know you are thinking your self how come an Eurofighter can match a F-22 in agility, give it fight and in dogfights beat it.
the answer lies in two factors,
Eurofighter has in a very low wing loading configuration a wing loading of 330 kilograms square meters, while F-22 something in the range of 400kg over square meters.
Eurofighter supercruises, so in a light configuration has relatively low drag even carrying external stores and weapons.
So why J-20 can not compare to Eurofighter?
The answer lies in two factors thrust to weight ratio and cross section.
F-22 is heavier than F-15 at empty weight F-15 weighs 13 tonnes while F-22 19 tonnes.
F-35 weighs 13 tonnes F-16 9 tonnes
all stealth aircraft are heavier than the generation before due to larger cross sections.
Why? first they use S ducts this increases weight, second internal weapons bays increase volume and weight.
now,
stealth shaping always increases drag yes i know you think J-20 is more aerodynamic than Eurofighter, but not Eurofighter has a bullet shaped forebody like Su-27 or any missile or ICBM.
However Eurofighter and Su-27 have a disadvantage
external weapons increase drag too, So J-11 or Eurofighter increase drag a lot fully loaded.
That is the reason Su-30MKI has thrust vectoring
So answer to your statement does J-20 need TVC nozzles? answer
yes it does.
Because the need to carry large weapons bays, add S ducts increases weight on J-20, plus its large faceted cross section increase drag.
So to answer you why Eurofighter can compete with F-22 in agility, the answer is at expense of weapons carriage, a light loaded Eurofighter can compete with F-22 in agility but only in a very light configuration otherwise it will not be able to compete.
However F-22 is not inferior to Eurofighter but that is thanks to TVC nozzles without it the F-22 is not better than F-16 or F-15, but with helmet mounted sights more or less both are even in dogfights.