This is a (pre-VT-X) limitation of the x86 design.
I did some googling, and it seems the rub is the segment register.
The Wikipedia article on x86 virtualization says virtual machine software (without VT-X) has to find certain instructions and patch them (they will not behave the same in ring 3 as in ring 0), traps a lot of stuff, and fiddles about with the segmentation register while it's running the VM to keep the VM's OS from modifying the trap handlers.
Really it's a pretty complicated bit of software.
With 64-bit mode, no segment register, so this became impossible.
AMD apparently added the segment register in 64-bit mode in later chips, so 64-bit OSes can run on them without VT-X, but otherwise VT-X or AMD-V is needed.
qemu-system-x64_64 will theoretically run whatever, but that's full emulation so it'll be rather slow.