You'd lose a lot and I'm not sure what you gain. Sans a few niggles here and there, WASM is pretty great for the web. It's small, lightweight, sandboxed, verifiable, fast to JIT, has fallbacks to ASM.js/stock JS, mostly easy to compile to, simple to build tooling for, etc.
The web is anything but small/lightweight and WASM requires a full blown JIT a la V8 to get good performance, so WASM being "small" (relative to what?) seems hardly a benefit.
JVMs are sandboxed and verifiable too, not sure what use a fallback to stock JS is but you can run a JVM in JS (look at TeaVM), it's way easier to emit bytecode for almost any modern language than WASM simply because JVMs do garbage collection for you and it's not really any easier to build tooling for WASM than any other VM.
In the end the main reason to do WASM over other VMs is that this way Mozilla/Chrome guys get to own it, instead of a competing firm.
WASM doesn't need a JIT, it needs a compiler. Unlike a standard JIT, you don't need decompilation and instrumentation. WASM is also designed so that browsers can reuse their JS JIT as a WASM compiler. Even from a JIT perspective, the difference between a lightweight JIT (eg. LuaJIT) and the heavyweight stuff used for JS is huge, and then the gap between JS JITs and Graal is a second such chasm. This equivalence is a false one.
Graal is not designed to be verifiable the way WASM is. We learnt enough from applets to not repeat that mistake.
GC is a distraction; WASM's opt-in is much better than Graal's by-default for use as a general compilation target.
WASM wasn't chosen disingenuously. Nothing else filled the role. If something did they would have used that instead.
You'd lose a lot and I'm not sure what you gain
So gaining java, ruby, R, python, etc support for the web are no gain ?
But the added value of graalVM is far beyond that, it revolutionize programming by allowing true polyglotism.
In economic terms, it would mean making accesible to the web millions of libraries which have a human/hours development cost of hundreds of billions of dollars.
Graal is a better target for these runtimes than WASM is, true, but Python-on-Graal is still a terrible target for the web. Huge runtimes with large memory footprints and startup times don't make for a pleasant user experience.
Polygot support, as extremely cool as it is, would be even less of a revolution inside the browser than it has been natively.
WebAssembly is the consequence of Mozilla not adopting PNaCL, and its advocates usually hand wave all the multi-language bytecode formats used throughout the industry since UNCOL, as if it is the very first of its kind.