That is true - it's probably more secure than storing them in the process, but several of these side-channel attacks can apply to kernel space (depending on hardware and security patches applied).
It's also not portable - OpenSSH runs on non-x86 architectures, and they might not have spare basically unused registers lying around.
Finally, I'm not sure the x87 registers have enough space to fit these keys. You have 8 80-bit registers, for a total of 640 bits. Your typical SSH private key might be 2048 bits or more.
So it's a fun and creative line of thinking, but probably not practical in this case.
It's also not portable - OpenSSH runs on non-x86 architectures, and they might not have spare basically unused registers lying around.
Finally, I'm not sure the x87 registers have enough space to fit these keys. You have 8 80-bit registers, for a total of 640 bits. Your typical SSH private key might be 2048 bits or more.
So it's a fun and creative line of thinking, but probably not practical in this case.