I don't have enough experience with XMM registers (and SSE4 in general) to know if this is actually {useful,possible}, but a hypothetical use might be creating and using cryptographic keys such that the important numbers are never stored in main memory. If e.g. a decryption key is ever present in RAM, it's probably possible to steal it with a cold-boot attack that copies all of RAM. Once you have the RAM dump, the key can probably be found very quickly:
for (secret_key_t *p = 0; p < RAM_SIZE; p++) {
decode_with_key(p);
}
This does require significant physical access, but it works. I seem to remember reading ~1.5 years ago about a turnkey forensics kit (bottle of refrigerant included) for doing cold boot attacks? Regardless, more ways to protect keys is could be really useful.
Registers may be stored to RAM (though there are often local register files in the CPU). If you're on a modern x86 platform, you may have encrypted memory support.
For Intel, look up SGX. For AMD, look up SEV. Each of these is way more secure than reliance on registers as secure scratch memory.
SSE registers will never get stored to ram without emitting explicit instructions (or getting an interrupt) to do so on any Intel/amd cpu as far as I know. It can be tricky to deal with such situations, but if you have a stretch of code where you can stop that registers can be used to hide data from memory.
That's why I said it's tricky to deal with interrupts, but possible if the effort is worth it to the use case. One could run the code in a kernel module which masked interrupts or use restartable sequences and cleared sse in the kernel when in certain code sections.
https://en.wikipedia.org/wiki/TRESOR