A little OT, but sometimes I think people are making arguments based too much on theoreticals and how western navies operate without fully considering the realities and likely operating areas where a PLAN task force might realistically engage in direct combat against a peer adversary.
Yes, 056As are not your classic modern blue water warship (although destroyers smaller were the workhorses of both the Atlantic and Pacific theatres during WWII), but where exactly does people think the PLAN would be fighting?
Probably for the next generation, the PLAN would not hold any delusions about their ability to go toe-to-toe with the USN far from home and win. Nor are there compelling reasons for China to go to war with America beyond its immediate home waters around Taiwan and the SCS.
It is because of these limited ambitions that the PLAN has chosen to make the 056A is primary ASW workhorse, and they will form the backbone of any PLAN fleets AWS surface element in any remotely realistic major conflict scenarios for the next two decades or more.
The lack of a full on hanger on the 056 would be an issue if they were meant to operate independently in an ASW role, but there would be only extremely unlikely and strategically irrelevant scenarios for that to happen. In most normal instances, they will operate as part of a much larger task group, and used as sonar screens as well as FOBs for ASW helicopters from the core fleet principle surface combatants. This intention can be easily seen from the large garage doors built into the aft superstructure, which would make perfect sense for refuelling and re-arming friendly ASW helicopters to extend both their operating range and endurance while minimising off-mission transit time to and from ships.
The existence of the huge 056A fleet could also be a reason why the PLAN is in no great hurry to retrofit all their 054A FFGs with the latest and greatest ASW hardware available.
When operating in such a role, it would make perfect sense for an 055 to act as the command ship for the 056A fleet elements due to its massive C&C capabilities.