I would imagine it would be really hard to make the voxel coordinate system spatially coherent over the whole planet, so placing smallish regions of buildable space at various geotagged points seems like a pragmatic approach.
You could still design it to get the types of interactions you're after.
Edit: To clarify I think it’s hard because of the earth not being flat but also because of the difficulty of syncing AR tracking to GPS tracking in a device independent way. You’d get a lot of error depending on how you attached the two reference frames together. Having many smaller buildable spaces means you can have lower accuracy from GPS but still make the world feel populated. The cubes wouldn’t align between volumes but the volumes can be in close proximity.
Good point about the coordinate system; you'd run into one sort of trouble or another if you want to go with anything that's approximately "cubes" (i.e. say each voxel is a "cube" of fixed height × fixed #degrees of latitude × fixed #degrees of longitude) unless you exclude two circles of the planet's surface from the game (say, some radius around each of the poles), and even then, you would have to contend with voxels having a different size depending on where on earth you are.
Possible (if off-brand) solution: a Minecraft based on the extrusion of an icosahedral tiling of the sphere [1], with voxels that are triangle prisms rather than cubes. Maybe an idea for someone who wants to design an AR game and does not have to sell it as a Minecraft variant.
Oh man - the thought of trying to build structures with "straight" walls using triangular prisms is giving me the heebie-jeebies. Entirely aside from the impossibility of creating smooth surfaces and right angles - I can imagine coming up with a pattern that reasonably approximates a straightness (to a viewer at a reasonable distance, just like Minecraft's current diagonal patterns [0]) at least on a local scale but which would quickly require somewhat ad-hoc and constant adjustment for structures past a certain size.
I assume the center of gravity of such a world would be the actual center of mass of however the voxels are arranged, meaning players could affect it with large enough structures or small enough worlds. Without adjusting "straight" "horizontal" structures to conform the curvature of the world, gravity would no longer be a force that was normal to the surface of the structure at some points on it.
I can also imagine people digging to the center of a world to find the gravity flip-flop point and playing with it. Or hollowing out the interior of the world in order to get a zero-G chamber (assuming no atmosphere) [1]. Or building gravity trains [2].
You could still design it to get the types of interactions you're after.
Edit: To clarify I think it’s hard because of the earth not being flat but also because of the difficulty of syncing AR tracking to GPS tracking in a device independent way. You’d get a lot of error depending on how you attached the two reference frames together. Having many smaller buildable spaces means you can have lower accuracy from GPS but still make the world feel populated. The cubes wouldn’t align between volumes but the volumes can be in close proximity.