This misses two key issues.
1. If you want to really trust that your crypto code has no timing side channels, then you've gotta write it in assembly. Otherwise, you're at the compiler's whims to turn code that seems like it really should be constant-time into code that isn't. There's no thorough mechanism in compilers like LLVM to prevent this from happening.
2. If you look at the CVEs in OpenSSL, they are generally in the C code, not the assembly code. If you look at OpenSSL CVEs going back to the beginning of 2023, there is not a single vulnerability in Linux/X86_64 assembly. There are some in the Windows port of the X86_64 assembly (because Windows has a different calling conv and the perlasm mishandled it). There are some on other arches. But almost all of the CVEs are in C, not asm.
If you want to know a lot more about how I think about this, see https://fil-c.org/constant_time_crypto
I do think it's a good idea to have crypto libraries implemented in memory safe languages, and that may mean writing them in Rust. But the actual kernels that do the cryptographic computations that involve secrets should be written in asm for maximum security so that you can be sure that sidechannels are avoided and because empirically, the memory safety bugs are not in that asm code.