Regarding sm6 ability to sink frigates, you may want to read this article (SM6 was one of the missiles that hit OHP). There are a lot of people with incentive to overstate it's anti ship lethality, because it's desirable to have a jack of all trade missile that can intercept everything and attack everything. With it's extremely high cost ($5 million per), this is a good way to justify continued investment and production in there. Keep in mind that standard missiles with secondary anti-ship missiles isn't a new development. SM-2s were commonly thought of in the same role. But I don't believe its uses sea-skimming mode, which means it's very easy to track and intercept. Therefore, it's main asset is just quantity. As our friend Patchwork Chimera would say, SM-6s launched from Burkes have wide breadth.
You really can't compare something like 055's Anti-ship and land attack capabilities to Burkes. Shilao's podcast compared 055 to both Kirov class and Ticonderoga class. I would entirely agree with that. The difference is that China can mass produce 055s and the Soviets could not mass produce Kirov class. The Chinese UVLS is significantly wider and deeper than MK-41. I'm also in favor of developing an even longer 11m variant in the future 055s. But even if they don't have that and just have 128 9m UVLS in the second batch, the attacking breadth of each 055 would be equivalent to several PLARF brigades.
All of which show the difference in the Chinese and Western philosophy in naval combat. With 055s, China is adopting a more Soviet approach in utilizing surface warship as the primary attacking platform. a USN CSG will be using Submarines, escorted B-52s and super hornets as main attacking platforms. The Chinese approach is basically designed to overcome PLAN's historical weakness in submarines and carrier operation via surface combatants. This is where China's ability to outbuild America in surface combatants really show up. It also plays to China's strength in missiles and C4ISR.
So if we look at a possible conflict against an equal or superior air wing, a Chinese carrier wing + nearby aerial assets will be mainly expected just to protect the fleet. They are likely to not be tasked with stand off attacks and ASuW until they can neutralize the attacking threat of opposing air wing first. The 052Ds and 054s are likely to be tasked with mostly AAW duties. ASW will be provided by MPAs, ASW helicopters and nearby submarines. In such a setup, a large portion of 055 VLS could be devoted to land attack and ASuW.
I think that's why they have been building 052D/054As on steroid. They need a good number of them to help protect the fleet. 055s are also capital ships. If you loose a few 052Ds/054As, it's not a big deal. If 055s don't get a chance to fire off their attacking missiles, that's a big problem.
Of course, a lot of this also revolves around them being able to lower the cost of production on long range hypersonic missiles and anti-ship missiles and even subsonic cruise missiles. If you combine high production of good missiles with 055s and ISR capability (through satellites and WZ-8 and High new series aircraft), you can deliver a lot of fire power against moving and fixed targets. It's surprising to me that many Western analysts haven't caught on to 055's importance.
Also regarding damage control, this is definitely an area that China had been behind on. 052D and 054A would generally still follow their earlier ship design principles. I would expect 075, carriers and 055 to be much better in damage control than 052D/054A. That's why I favor the need for a new class of destroyer to replace 052D. I would also expect 054B to have significant changes that will have better damage control design, greater automation, larger berthing section (for long deployment) and more modern propulsion compared to 054A. If a warship gets hit by SM-6, it really should be able to continue to operate (unless the strike hit a sensitive spot).