Hey, this is also my interest. I was just looking into whether it was possible to e.g. build an archive extractor that runs like a normal program but does the actual extraction completely in wasm. Unfortunately, AFAICT it's possible but requires custom code; you can't (yet, I hope) just compile unzip/libarchive/whatever with CC=wasicompiler and get a sandboxed binary. But we're getting close.

What do you mean? You absolutely can run compression in WASM.

For example here is Gzip in WASM: https://github.com/ColinTimBarndt/wasm-gzip

You should be able to do exactly that though? Why do you think you can't?

You will of course need to include a lot of support code to provide the relevant syscalls and otherwise emulate the environment that the code expects. But there are plenty of examples of that at this point.