The problem is that ISAs don't support any sort of side-channel resistance mode, so even hand-rolling assembly (or machine code) won't fix every possible leak.

The problem is that ISAs don't support any sort of side-channel resistance mode, so even hand-rolling assembly (or machine code) won't fix every possible leak. If such a mode could be added, then any language could add appropriate intrinsics to set it. More likely is that cryptography-specific instructions (like AES-NI or ARM's SHA hash instructions) will get added for more relevant operations.