I don't understand your argument about lack of J-20s. If China cannot produce enough J-20s for multi role missions, why would it be able to produce sufficient JHXX?
Assuming all planes are equal (which they're not) but just to reply to this particular question: Because real world politics. Because one can't expect that Xian or SAC will ever be given to produce J-20s. Or that CAC will be given so much funds that they triple their production of J-20 while at the same time Xian and SAC get their funds cut (as funds are finite, so if CAC gets more, others will get less)
The reason why a VLO platform is needed for delivery is because the mission requires close in delivery. If standoff delivery is to be employed then a VLO platform is not needed. Just send in a J-16 and fire off from 500 kms away.
I absolutely agree on close in delivery needs. But standoff delivery is not all the same. Say one has a missile with nominal range of 300 km. What if the enemy has air defenses and interceptors positioned 200 km in front of the target. Suddenly the plane needs to get to 100 km of the enemy defenses. VLO may stand a chance there where non VLO won't.
I think we will have to be patient on this and wait for its unveiling to determine if your postulation is correct or not.
There's no question that a larger airframe that is primarely designed for a strike mission is inherently more capable of achieving more range, more payload and better stealth. That doesn't need to be proven.
There is a reason why there is no conversation about fitting a JASSM or a LRASM unto the F-35. It is because long range stand off weapons do not need a F-35 for delivery. It is the reason why the F-18 and B-1s are integrated to employ them.
Another thing with stand off weapons is that range often isn't used in a straight forward way. If the target it 300 km away, one won't just launch the missile and have it go down that shortest, most obvious route. Especially if we're talking about stealthy missiles. Rather, those JASSMs will go along various waypoints around the target, possibly crossing even double the distance, in order to reach the target from less expected and thus less monitored/defended directions.
F-35 will definitely be carrying JASSMs one day, too. Externally, of course. It'd be even better for it if it could carry them internally. JSOW and JSM are one of the main weapons for F-35C for example, even though both are stand off stealthy weapons.
J20 will make a very decent striker one day. Perhaps even as good striker as F-35 or better than it. IF indeed 1000 of them can be put into service within a decade, a separate JHXX is certainly not as important. But it's VERY unlikely we'll see such production numbers in such a timeframe. So IF there's money to go around to XAC or SAC, besides H20 and J31, one can still do better for strikes.