That's why traditional operating systems have processes that can't access each others memory. WASM instances don't have this sort of "internal isolation", anything running in the same instance can access all memory in that instance, memory safe language or not.
Again, language-level safety doesn't matter here. It makes a lot of sense to write the sandbox itself in Rust, but it must not matter whether code running inside the sandbox is written in Rust. If that would be required, the sandbox has already failed.
It very well can:
For example, let's assume you have a graphics editor running in the browser that stores files in the cloud. If it uses a vulnerable C library to decode image data, an attacker might be able to play havoc with your files despite the sandbox never technically having been breached.
This can be mitigated by either using a safe language, or having the decoder run in an isolated wasm instance. Either way, you have to design your application with these considerations in mind and can't just take arbitrary, potentially vulnerable applications, compile them to wasm and be done with it.
Apart from that it would be quite a feat to use internal memory corruption for anything useful in WASM, because both the code and callstack live outside the sandbox and are not accessible from within (e.g. tricks like return-oriented programming are not possible in WASM.
Instead of popping up an alert, you could have requested the deletion of all files in the cloud storage.
I also wonder why stack canaries wouldn't work on WASM, since the compiler creates stack frames on the data-only stack just the same (but maybe Clang's `-fstack-protector` doesn't work for some reason in WASM, I'll actually need to check that).
WebAssembly sandboxes apparently are going to sort out all security issues in modern computing.
For example, if you corrupt a program that's allowed to use web sockets, you'll be able to port scan the user's local network.