asm.js (the spiritual precursor to WASM) worked pretty much the same, and an awful lot of languages were compiled to it.
WASM does provide a more predictable compilation target to be sure, but I don't think it actually opens any new possibilities re what languages can be compiled.
Multithreading and 64-bit integers come to mind as creating difficulty, and I imagine "raw" memory buffer access having much higher latency to the point where it's completely impractical. For example, a quick search gave me this library [1] that compiles FFMpeg into Asm.js but the author says it is almost a factor 10 slower. Asm.js would also become extremely verbose for any larger code base (imagine compiling a AAA PC game to Asm.js).
It may be as you say that there are no new theoretical possibilities being opened by WASM, but to me it is a natural step forward to resolve inefficiencies and ergonomic problems in ASM.js and make it all less painful. And hopefully WASM won't be frozen in time either - the platform needs to keep improving to make more use-case scenarios practical.
asm.js (the spiritual precursor to WASM) worked pretty much the same, and an awful lot of languages were compiled to it.
WASM does provide a more predictable compilation target to be sure, but I don't think it actually opens any new possibilities re what languages can be compiled.