I think the major reason why the PLAN continues to build more 054A+ is to make up for their ASW weaknesses you described. It is the most economical and effective stopgap they have, though I think they made a mistake underarming the 056.
Giving 056As the same TAS and VDS suite as 054A+ and 052D, as well as seemingly replacing the AShMs with long range ASROC, and mass producing 056As is probably one of the most significant decisions in improving their regional ASW capabilities over the last few years.
Remember what the 056s and 056As are replacing (037 variant subchasers) and they will be supported by 022 FACs, land based air power for air cover and maritime strike, as well as probably a number of frigates during operations, not to mention ASW MPAs as well. 056As will not merely be a stopgap, but will operate in conjunction with currently developing and early fielding ASW capabilities and will likely remain a key role in the Navy's regional ASW forces, at least within green water range.
The requirement for heavily arming a ship of 056/As size with AShMs is simply not there given the way they will probably be operated. But giving them a potent ASW sensor suite, and then mass producing them in large numbers OTOH is a capability that will significantly enhance the Navy's overall capability. In context, 056/As AShM armament is barely a criticism worth noting IMO.