Of course, modern processors don't really care about register-register moves because they have hundreds of hidden intermediate registers and register renaming which makes those types of moves "free." (e.g. Haswell has 168 GP registers, only 16 of which are exposed through the AMD64 ISA.)
In any case I believe the point of the GP is that any necessary copy can be done by going through memory, so register-register moves can be dispensed with where minimalism is the goal.
mov 0x1000(%rax,%rax), %eax
mov %eax, 0x1000(%rax,%rax)
mov $7, %eax
0000000000000000 8b840000100000 movl 0x1000(%rax,%rax), %eax
0000000000000007 89840000100000 movl %eax, 0x1000(%rax,%rax)
000000000000000e b807000000 movl $0x7, %eax