Another big issue is the intakes on the J-20. These need substantial modification once WS-15 is ready; if you look at the F-35's intakes, these are roughly 1 m^2 inlets once DSI is factored in. The inlets on the J-20, once DSI is factored in, is around .67 m^2, which is what you'd need for AL-31F and WS-10.
The result is that once you have the WS-15 ready, you have two options and suboptions for one option:
1- The WS-15s choke under some pressure and airspeed conditions, because the inlets aren't large enough to provide sufficient oxygen for their operation. This happened with the F-14, where the upgraded engines were much better than the original engines, but weren't completely usable (max speed didn't change much) because the inlets weren't big enough to give the new engines their full oxygen needs.
2- The J-20 inlets are redesigned, allowing the WS-15 to perform fully. There are two ways to do this
2a. The first way is simply to shrink the DSI, which would affect the inlet performance at certain altitudes, airspeeds, and AoA. Moreover, the inlets would still not be large enough; you'd need a full fixed inlet to get the 1 m^2 inlets needed for the WS-15 to function fully.
2b. The second way to do so is to enlarge the inlet. That is going to affect stealth and aerodynamic characteristics of the J-20, effectively being similar to a full modification of the J-20's fuselage. You can lengthen it horizontally or you can lengthen it vertically, which would mean that the bay depth of the J-20 is now increased.
If 2b is selected, this is pretty much a harbinger of a J-20 strike variant. You might as well modify the J-20 so it can carry a Kinzhal-class missile in its weapons bay, if you're going to increase the fuselage thickness, and this entire enlarged weapons bay can also be used for other strike missiles and AAM, putting its AAM payload for cost as equivalent or better than the F-35.
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Another factor is, well, the alternative to a strike J-20 is the JH-XX, but how do we know whether the program will mature fast enough? The PLAAF, whose primary role is air defense, is unlikely to develop a large JH-XX inventory so the PLAAF's strike capability will be impaired. On the other hand, a strike J-20 can perform both air defense and strike functions, complementing the JH-XX. A strike J-20 would increase both China's air defense capability and strike capability at the same time, forming a bridge of versatility between the conventional fighter J-20 and the strike-only JH-XX, which looks more designed as a light bomber.
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Finally, note the difference between the F-18 and the F/A-18E.
It seems as though the F/A-18E is virtually a new aircraft, with very little inherited from the F-18. But the F/A-18E was still prototype to IOC in 3 years, compared to the 5 years of the F-18.
It's going to be easier and faster to radically modify the J-20 for new roles than to come with a complete clean-sheet aircraft like the JH-XX, and the J-20 can still provide the JH-XX a back-up should the JH-XX see unexpected delays as with all stealth fighters.