What about defeating supersonic or hypersonic cruise missile strike against ships in the high seas? Are Chinese type 055 ships only expected to fight within the first island chain?It is a matter of requirements and needs. You procure based on what you need. US faces a ballistic missile threat from their adversaries, so it makes sense for them to have missiles such as the SM-3 and SM-6 for BMD defense. All these platforms already exists in China bar an SM-6 all-in-one like missile, which really isn't needed anyway. China doesn't face any ballistic missile threat so there's no need for an SM-3 or SM-6 like missile. It's not unlikely that they may make a naval BMD missile in the future, but it isn't currently needed or a priority.
In a war, US is most likely to saturate First island chain choke points into Gibralter like fortresses with enough shore based firepower that chinese ships cannot get outside without significant damage. Just breaking that blockade needs very strong defense against missiles.