I wonder if it is possible to avoid "digging deep" problem by first building a cube out of voxels and then applying the type of distortion that turns the cube into quad sphere not just to the surface of the cube but also to the insides of the cube.
I don't know how to explain it better, perhaps I should try to write some code, lol
It seems like the easiest way would be if you hit immutable lava at some point.
I see what you mean. An assumption in Minecraft-style games is the character stays the same size, but this needn't be the case. Your character could get smaller the further you dig down in order to match the decreasing size of the interior voxels. This would even create a kind of forced-perspective effect when looking down a hole, as objects at the bottom would look far more distant than they really are.