Javascript is a safe language, but it's powerful enough to exploit Spectre and Meltdown. Rust would be the same. It's not badly-written programs we need to worry about in this context, it's well-written malicious programs exploiting badly-designed hardware.

We don't need apps written in safe programming languages to fix this problem, we need secure browsers, OSes and hardware. (And yes, those bits should be written in safe languages.)