Most of those are of the form "malicious code delivered as Java applet can break out of the JVM sandbox". That is, they crucially rely on running untrusted code. By contrast, the threat model here involves attackers subverting existing, trusted code. Memory safety holes in Rust overwhelmingly rely on bizarre carefully crafted code that nobody would accidentally write.
There are some exceptions: Java is affected by serialization issues along the lines of the Rails YAML vulnerability, for instance. But most of those don't apply to Rust either for various reasons.