As mentioned in other replies, this doesn't fully solve a lot of the cases. I think z order curves might actually be better here, they are slightly less accurate individually, but in a way that would seemingly minimize the worst case results when taking the minimum of the two. But at that point you are probably better off using a single z-order curve and using the coordinates to check the manhattan or Chebyshev distance using bitwise operations.
I would second the use of Z-order curves. Hilbert curves were famously known as more optimal on spinning disk in a specific context a few decades ago. Inertia has kept them top-of-mind even though modern systems do not have the problems Hilbert curves were better at solving and those curves are more complex to use than e.g. Z-order curves.
