Production capacity is unlikely to be a primary factor, since as pointed out, they could expand CAC or even subcontract/work share with SAC.
It would take considerably less time and expense to expand production capabilities than finishing off the J31 design AND also set up a seperate production line for that also.
What might be a more significant and hard to bridge capacity gap might be in terms of the design team.
From various comments on the J20 from officials and members of CAC, we know that the PLAAF and CAC have a lot of long term plans to continue to develop the J20. Potentially with new variants, purhaps along the lines of the aborted FB22 where a more dedicated strike variant is developed.
In addition, the PLAAF is likely to keep CAC busy for years to come as they learn more about the J20’s capabilities and limitations and wish list changes and modifications. Not to mention the upcoming WS15 integration work.
But OTOH, designing a carrier capable J20 will also be a significant undertaking that will require potentially years of the J20’s design teams time.
As talented and as capable as CAC and the J20 design team are, I would seriously doubt they could take on both those fronts at the same time.
It could well be that there is a bit of a turf war going on behind the scenes between the PLAAF and PLAN, with neither service prepared to have their needs come second place.
The PLAAF has first dibs on CAC’s time by dint of already having the J20 as their official backbone project. So rather than potentially having to wait years before CAC even starts serious work designing a carrier J20, the navy could have decided to go with the J31.
There would have also probably been significant political support for the navy choosing SAC as a means of maintaining a real competitor to CAC to keep their on their toes.
That political support may well come with additional funding and/or pull to get CAC to share key J20 tech with SAC to help ensure the J31 is technologically competitive with the J20.
Hopefully loosing the PLAAF to CAC has served as a much needed wake up call for SAC, and they can make the most of every advantage offered and this lifeline and up there game significantly. Because I think this is probably their last big chance.
If they screw up with the J31 naval contract, China would be better off building up one of the other main aviation firms up as an alternative fighter maker to CAC and let SAC die.