ECIES is quite fine though for most asynchronous applications, where having a signing key also makes sense as you often want to publish long-lived, signed data and build a trust chain (e.g. generate and sign session keys from a master key). I built several real-world systems based on that (e.g. [1]) and they all made it through the audits fine. I was exploring Noise-based protocols but I find it's best to rely on primitives that are supported by the Web Crypto API.
ECIES is a hybrid encryption construction; Noise is a protocol. They're two different levels of abstraction. This thing we're commenting on has a protocol; it's just an accidental one, which is usually not what you want. WebCrypto doesn't provide a protocol framework, just a bunch of primitives.
