Imagine passing a pointer to the backing store for Rust or Go arrays across an interface boundary. Imagine a JavaScript implementation also written in either of those languages, but where the entry point interfaces prevent the language (caller or callee) from tracking and ensuring lifetime invariants across the boundary (certainly not statically, nor dynamically because we're not using a unified abstract VM like the JVM or CLR). Correct memory management necessarily relies on the programmer explicitly and manually synchronizing liveness between those distinct environments. If they get it wrong it's not Rust or Go's fault, nor can you squarely lay blame on either side of the interface boundary; it's the programmer's fault and/or poor interface design; and the likelihood of such a bug is equally likely in Rust, Go, or C++.
JIT also comes into play because even if the entirety of Chrome or Mozilla were nominally implemented in Rust or Go, the compilers and runtimes of either language could not ensure correctness of the generated JIT'd code nor track dependencies across native Rust/Go code and the generated JIT'd code--particularly for JavaScript code where the norm is object lifetimes escaping function scope. JIT'd native code effectively, if not formally, results in two distinct, disjoint runtime environments. Correctness, again, would be predicated on correct use of interfaces that might look suspiciously like malloc/free. The better interfaces would expose and emphasize the semantics of anchoring and referencing binding directly, but such interfaces are difficult to design and implement--after all, if they were then the argument that safe C++ is too difficult in practice wouldn't have such weight.
There are entirely interpreted JavaScript engines. Rhino is a obvious example for Java. Duktape is a nice, embeddable interpreter written in C. Theoretically it could be rewritten in Rust, but that wouldn't make it any more likely to displace implementations like V8. And that's my point. In reality the fundamental problem isn't that we're not using a Rust-written Duktape (it's manifestly not a realistic expectation, not in the domain of JavaScript engines), it's that we don't invest enough attention in integration across inevitable language boundaries.
This is not feasible in C++, because the language isn't safe to begin with.
But that can never happen if the WASM specification insists on semantics that all but require tight integration with the browsers' JavaScript engine and GC.