Just to clarify my personal opinion, I hope at some point in the future we could provide builds that don't depend on WASI, similarly to what other projects such as rustwasm and AssemblyScript do. We don't depend on WASI because we want to, but because it was the quickest way to make things work. Swift stdlib despite being somewhat minimalistic (as in, shifting more responsibilities to the Swift Foundation library), still assumes the presence of ICU and libc. While the swift-embedded project shows that you could avoid bundling ICU, for a libc-less build we need to write our own custom memory allocators and stuff like that, which is not currently feasible with only a couple of contributors that SwiftWasm has. Everyone is very welcome to join and kickstart work in that direction though.
As as a side-note, the name of our project is SwiftWasm, or "Swift for WebAssembly" if you prefer a less concise version. While "WASI" is an acronym, "wasm" is not, and it looks like rustwasm people follow that convention too 