The Sylver VLS and the Aster 15 and 30s definitely limit the Daring class to air defence but in this field it supposedly is second to none, if range of missiles are ignored. Then again as a purpose designed destroyer to fleet defence, Asters have enough range. The RN's doctrine is similar to the USN's - centred around a carrier fighter wing that can perform various missions. Everything else on the surface is to protest those carriers and perform some limited anti-surface roles itself along with a comprehensive anti-sub warfare in combination with airborne assets. So comparing them truly is inappropriate. Personally I think this doctrine is superior to the "Russian" one which is just spamming the ocean with capital ships armed to the teeth lobbing hundreds of anti-ship missiles with subs performing a secondary role to supplement this effort while countering enemy subs.
We have seen PLAN shift towards the US doctrine since it selected the air defence focused Type 052C over the Type 052B and invest heavily in a strong future carrier fleet with the rest of the surface fleet serving as multirole ships but also primarily air defence eventually, when matured CATOBAR carriers come along with the entire air wing they'll carry. For now PLAN is still very much giving 055's multirole status and they clearly want these heavy destroyers to serve both doctrines well. China's always taken what it considers the best from Russian thinking and combined it with American while mixing its own in too. The perks of catch-up position. The matured Type 055 will probably get quad packed medium range SAMs to add to existing repertoire. Maybe a railgun and ballistic missile defence or ASAT missiles similar to SM-3 as well. That's going to be a Kirov + AB III with a railgun.
Don't let the large Russian ASMs fool you. The Kirov and Slava classes are rich in both long range (S-300 RIF M) and close range air defenses. The Kirov class has 96 S-300s, and the Slava class has 64 S-300s. In addition the Kirov has over 100 short range missiles, the Slava class has around 40. The number of antiship missiles on the Kirov class is only about 20, even if they are big, and the Slava class about 16, even if these are big. So these are ships that lean much more to air defense. In role they are comparable to the Type 055, and are intended to escort the planned Russian aircraft carriers. The Soviet ships were quite balanced and multirole, just that the Western ships, antiship development is stunted for budgetary and political reasons. The US did have a developmental project for a supersonic missile called Sea Dragon, something that were hidden all these years until exposed by hackers. The Sovremenny destroyers are also balanced for their air defense and offensive capability, while Udaloys are specialized ASW ships.
The 052B is also a balanced ship, 16 antiship missiles with 40 SAMs. The 052B didn't really disappear into a dead end but rather, morphed into the smaller Type 054A frigate. The Type 054A is a scaled down 052B with less missiles. 052C/D inherits the idea of the Sovremenny's antiship capabilities, with eight large YJ-62 on the C, and an unknown number, possibly 8 to 16 YJ-18 on the D. Along with that, they also inherit the Sovremenny's OTH antiship sensor by copying the Mineral-M system which consists of active radar, passive sensor and CEC into the Type 366 and tweaked improvements on it. This system equips every 054A, 052C, 052D and even the refitted destroyers today. That's plenty of ships that inherited this gene from the Sovremenny.
The lack of "balance" in Western ship designs, i.e. antiship capability, comes not from design or policy, but by budgetary cuts and institutional neglect. Even among European frigates, the ship designs appear to have extra space for adding more antiship missiles but never happened. Now the US is rushing antiship capability pronto, with LRASM and NSM, dual use Tomahawks and even converting SM-6 for dual roles with antiship.
