Re:
This was always part of soviet tactics for when ships approached closer to land, it is why they kept investing in Kilos. Whether a carrier group needs to get that close / pass through such shallow water to get to China in the event of an unlikely war with China, I don't know. Given the potential loss of lives if a carrier was knocked out, I doubt it would ever happen. Chinese submarines already pose a real threat to carriers though in all waters, as the Admiral pointed out in the article I quoted. Only one has to slip through. The carriers will be kept well away from the action if such a war ever breaks out with China, they are too important for projecting power (not to mention the potential loss of lives) to risk losing against a more credible navy than most potential opponents have.
Actually, the primary Soviet sub-weapon vs US carrier was the sub-launched missile starting with the P70 ametist for the charlies and which gradually progressed to the Oscars equipped with 550km ranged P700 granit cruise missiles.
The premise was simple. The longer the missile range, the greater the search area of the carrier-borne ASW. 2 times the range = 4 times the search area. Search can focus at circumference but no one can cover 3455 km of circumference with just 1 CBG at 550km. Worse at 550km range, you're talking about 1 million sq km of seach area if the sub gets past the searches at circumference. You can't cover that same area with 2 defensive SSNs either.
Of course the further the missile, the more reaction time for SAM defenses. So missile research focussed on speed. The faster the missile, the less reaction time. In the 80s it was far worse for US CBGs as escorting SAMs had very limited range. Hence the development of standard SAMs to its current range today.
At the same time, since one or more SAM can probably take out one ASM, you need to fire enough ASMs to overwhelm SAM defences, the idea was to put as many into a sub as possible, hence the large oscars which carry 24. The attacker had the benefit as the CBG had to dilute its escorts to cover 360 whereas the attacker can concentrate its forces in a standard direction of attack/attack vector, conduct decoy in other directions or conduct simultaneous multiple attacks eg in coordination with air aviation. Hence the development of aegis to coordinate defences.
China's sub-launched missile capability is in its infancy. YJs don't have the same reach as the russkis yet, Kilos only carry 4 missiles and SSKs don't operate as well in open ocean as the SSNs due to endurance limitations. SSKs works well in the littorals which has been discussed many times before.
Even in the air, the same principle applies. The further out from the CBG, the more tanker support required. CBG can ill afford to send its entire air wing out to a single vector when there is a possibility of attack from another.