The lowest-level routines need to be written mostly in assembly to have constant-time execution (which is a difficult task even in assembly due to the complexity of modern CPUs). None of Rust, C, nor C++ can guarantee constant-time execution, and all three have aggressive optimisers that can remove "useless" code that is meant to defend against side-channel leaks.

However, there's more to TLS than just the lowest-level primitives. There's parsing, packet construction, certificate handling, protocol logic, buffer management, connection management, etc. These things can be written in safe Rust.