My intuition is that the problem is in using squares for the error. The volume of space available for a given distance of error in 3-space is O(N^3) the magnitude of the error, so an error term of O(N^2) doesn't grow fast enough compared to the volume that can contain that magnitude of error.
But I really don't know, it's just an intuition with no formalism behind it.
But I really don't know, it's just an intuition with no formalism behind it.