I don't think China has a need for something like that. The Type 056 is already a pretty decent design, it is a corvette, not a frigate.
I agree that 056 is already "pretty decent" and should not be tinkered with too much, which is why I am advocating for a minimal cost change that would significantly enhance the capability of the type in the roles it already fulfils. Really, going from four to eight cells should be <2% increase in total lifecycle cost for ~50% increase in ability to prosecute surface and sub-surface threats. Why wouldn't you do this?
Unlike Russia which seems to stuff its corvettes to the gills with weapons because they have no larger ships and their shipyards suck
Even at the height of the Soviet Navy, it fielded many well armed small combatants and this owes to Russia's complex naval geography with high-end threats (surface, subsurface, land and air-based) at relatively short ranges. If the Soviet Union were ever in a position to field larger combatants on the scale of USN (or tomorrow's China) then the need for such vessels would decline somewhat, but that was never a realistic prospect. In all realistic scenarios past and present, well armed small combatants are an important part of Russia's overall naval force structure and this is not an artifact of a temporary lull in the construction of medium/large combatants.
056 was never meant to operate far away from the shore or being the one to hand out the killing blow. In an actual shooting war it will most likely remain comfortably under the cover of land-based aircraft and coastal missile batteries. Its main mission will be to secure/guard the littorals, allowing larger combatants to do the actual fighting. Alternatively, within the 1st island chain, it could be deployed under the guidance of larger destroyers to swarm/bait/distract the enemy as to create opportunities for other units to strike. If a 056 ever finds itself needing more that 2-4 Yu-11 or YJ-83 then there is something seriously wrong with your war fighting strategy.
I agree that the primary wartime role of 056 is to serve as a sensor node, with most actual target prosecution done in coordination with other assets, but that only goes so far. As above, considerable resources have been invested in creating this platform and operating it, so why would you not spend a tiny bit more to generate an outsize increase in its ability to engage surface and subsurface threats?
If the loadout is 2+2 YJ-83/Yu-11 then that gives the 056 precisely one shot at each type of target, because any engagement should consist of at least two shots to allow for mechanical or guidance failure, jamming, etc. Indeed, the more I think about it, a 2+2 loadout seems unworkable. With only four cells, the only sensible wartime loadout is either four YJ-83 or Yu-11, and accept an inability to engage either above or below the water. Maybe the 056s routinely carry YJ-83s and the 056As Yu-11s.
Will reply to your posts later, Tam.