These things are very new to PLAN, and just having a first generation product is not enough, the effectiveness of these TAS and VDS is questionable, things have to be improved over time and over actual operations. Same goes for the experiences that NATO members have gained in WWI, WWII (all that experiences with U boats are not for nothing) and over the past few decades - during which time PLAN had never been serious on ASW (well they practically did not have a Navy after the Sino-Japanese War and before the end of WWII).
The PLAN was very new to AAW and high end air defense as well before the introduction of 052C. Since then they've commissioned additional 052Cs and even more 052Ds and looking to build more 055s. This is all despite having iterated from much less capable systems such as those present on 052Bs or 052s and 051Cs.
I think this shows the PLAN do not tend to procure new ships with certain subsystems in large numbers unless they are satisfied to it to a certain degree.
The 346 APAR on 052C technically was a first generation product as well, yet they were satisfied enough to produce an additional 4 hulls of it, as well as to further develop variants of it such that it has become the mainstay shipborne APAR family in the PLAN's surface combatants.
Considering how widely the PLAN have profilerated the same type of VDS (and likely TAS) across the 056As, later 054As, all 052Ds and all 055s, I would suggest that their "first generation" system may not be as immature or incapable as you fear. This of course is on top of the fact that the PLAN did have chances to evaluate certain European systems when they were imported as well.
ASW is indeed a challenging art for everyone, but in the last decade or so the PLAN have significantly stepped up both the qualitative ASW suite many of its ships have, as well as advanced the quantity of those ships in service. Few navies have widespread fielding of ships with both VDS and TAS (aka "two tails") as the PLAN have done, in particular in the last year.
To quote myself from last year:
"A review of the numbers show the PLAN surface combatant fleet fielded zero two tail surface combatants prior to March 2014. Slightly more than four years later, as of September 2018, there are about 42 two tail warships in service, of which about 20 are 056A corvettes intended for near-seas missions, and 22 are blue water capable 052D DDGs and 054A+ FFGs."
In four years, they commissioned forty two ships with VDS+TAS suites.That number has of course grown since September 2018, as additional 056As, 054A+, 052D and 055s enter service.
This is on top of other, previous ships many of whom have had single tail TAS as well.
The things you have pointed out certainly helps (especially the introduction of 056A with towed sonars), but they are far from enough to be serious on ASW. Japan have been having helicopter destroyers for decades, with each accommodating 3 or more ASW helicopters. Few PLAN destroyers or frigates carry more than 1 helicopter even at much higher tonnage. For the 056, other similarly sizes corvettes like the 1300t Sa'ar 5 have a hangar, the 1800t Braunschweig class has hangar for 2 helicopters. This indicates just how much PLAN doesn't care about helicopters, or ASW in general comparing to other priorities, or other Navies. This lack of capability or awareness is quite astonishing for the 2nd largest economy/Navy in the world.
For naval ships, ASW capabilities can be divided into two categories:
1: Organic shipborne capabilities, such as onboard sonar the top end of which today is VDS and TAS, as well as hull sonar; and also things like VL ASROC type weapons, and less direct flank capable torpedo launchers. In this domain the PLAN have made massive advancements, with the widespread proliferation of VDS and TAS, as well as with the introduction of VL ASROC weapons on 054A, long range flying torpedo/ASROC weapons on the 056A (and presumably other ships that can carry YJ-83s as well).
2: Aviation capabilities, namely ASW helicopters. In this domain the PLAN obviously have yet to advance as far as the previous, but that is because PRC helicopter manufacturing capablities have yet to reach a level whereby they can meet the entirety of the PLA's needs (Army, Air Force, and Navy). Specifically, the lack of a true 10 ton medium weight helicopter that can be mass produced has hindered surface combatant aviation. This is not a reflection of the PLAN "not being serious" about ASW but a reflection of industrial limitations.
For the PLAN, it seems obvious in the last decade or so they've significantly advanced their ASW capabilities in the domains when it was technologically and industrially feasible.
The fact that they've given a ship as small as 056A a full suite of VDS+TAS is absolutely mind boggling and if anything that is indicative of just how serious they are about ASW. I can't think of any other surface combatant as small as 056A with a VDS+TAS, let alone one produced in such large numbers.
It would be preferable if they were able to mass produce a large number of ASW helicopters as well, however if industry is a limit there is nothing one can do to bypass it.
Yet even despite the limits of not being able to mass produce ASW helicopters, they have still made a frightening amount of progress in such a short time in terms of organic shipborne ASW capabilities.
You mention the JMSDF having helicopter destroyers, which is certainly true and fairly unique to their navy. However their primary surface combatant destroyers -- even their largest and most capable Atago and Maya class destroyers -- only have one helicopter hangar as well.
Furthermore the 1800 ton Braunschweig class certainly does not have a hangar that can accommodate 2 helicopters -- it is only capable of accommodating 2 small helicopter UAVs, not full size helicopters. In fact I'm not even sure if that ship class has a hangar capable of accommodating even one actual full sized helicopter:
Furthermore, corvettes like the K130 and even the Sa'ar 5 are somewhat different to the 056/A; those ships are designed with different armament, sensor fits and in the case of Sa'ar 5 are designed with different missions in mind than what the 056/A looks configured for.
Looking at the 056/A it seems obvious that they deliberately made the stern higher so as to give it the ability to carry VDS+TAS rather than to make the stern lower so as to accommodate a helicopter hangar instead.
Submarines are effective submarine hunters, it is no secret how noisy PLAN subs are. And while we see PLAN advances in many areas, quiet subs is not one of them. We can safely assume how noisy the surface combatants are if we know their subs are noisy. So many decades have past since the Soviets and the US competed on advanced submarine technology, yet I wonder does PLAN even care about it?
PLAN nuclear submarines are obviously likely much less capable than their US, European and Russian counterparts and that is largely accepted, considering the original 09IIIs were built in the 1990s and the 091s even older. The fact that they were much less competitive than their foreign peers is to be expected.
We know that a new generation of nuclear submarines are currently being constructed and likely to be mass produced, but it will be a number of years until we get any hint of how competitive they may be.
PLAN diesel submarines are generally regarded and acknowledged as fairly competitive abroad.
Chinese nuclear and diesel submarine capabilities are generally not conflated together because of the above reason, so I'm not sure why you are doing so here.
It looks to me their priorities are more politically motivated - building large and visible surface combatants like the CV, 055, 071, 075 that would impress the man in charge as well as be the pride of the nation, while the value of a large fleet of blue water amphibious ships like the LPD and LHD to PLAN is questionable. It appears the Navy does not really know what they want or need for larger ships, and is just following what the USN does - the USN built the Burke, they come up with their own 052C/D "Aegis", they don't even bother to design it a little differently like the Type 45 or other European AAW destroyers with AESA. The USN built a 25,000t LPD, they came up with a 25,000t LPD that is the equivalent of San Antonino class. And the 075 would probably be 40,000t, just like the WASP/America classes, unlike other Navies in the world that would build according to their needs.
I think you have gravely misunderstood the extent to which the PLAN have advanced their ASW capabilities.
I wrote this article quite a while ago, but it is still certainly relevant. Considering how little you seem to know about PLAN ASW advancement, I think you most certainly should be aware of its contents:
I also question why you believe the PLAN's procurement can be described as not really knowing what they want or need for larger ships and that they are merely following the USN -- have you considered that perhaps their ships and their procurement is intended to match their own requirements, and that such solutions happen to better resemble certain existing ship types than others?
To be honest, you are throwing out a lot of big claims in your post and I wonder how familiar you are with the actual content. Mistaking the K130/Braunschweig class as having a hangar that can accommodate two helicopters, and conflating PLAN SSNs and SSKs together, and assuming that because the 052C/D look similar to Burkes that they had not considered what their actual own requirements are meant to be?