No, the air superiority problem arose when China soon built a 5th generation twin-engine low-visibility aircraft. For this reason, the single-engine F35 was insufficient for the Far East countries.
Well, if the f35 is such a beautiful war machine, why do you spend money and time building a new TWO-ENGINE 4,5 GENERATION aircraft instead of buying more?
The manufacturer of the F35 has even reduced the number of F35s it will buy in the USA, it is developing the F15 and buying the F15 ex. In fact, research, while the USA has the invisible flying computer, the magnificent F35, it continues to buy the single-engine F16. I wonder why?