Why can I see tiny gaps after extruding an object together?

I wanted to make a cube with inside walls (thickness), so I came up with this design (wireframed):



I started with a 0.12 x 0.12 x 0.12 cube and extruded faces until I had a 1.2 x 1.2 x 1.2 cube like this.

The problem is, there are tiny, tiny gaps visible where an extruded face meets another face:



It's difficult to see but they're there. Very annoying!

Anyone know why?

Even if I build the cube in a different (better) way by making a frame like the first picture, then adding 0.8 x 0.8 x 0.12 walls, the gaps will be visible.

 

Yes, ProGrids at 0.12 and everything is welded.

I've built a (much) bigger cube the same way and it doesn't display any gaps, so I'm thinking ProBuilder doesn't work at really small sizes. (Wouldn't be the first bug I've encountered.)

Here's my entire build process which can be easily replicated:


Start with a 0.12 x 0.12 x 0.12 cube.


Grid snap at 0.12 and major line at 10 to create a 1.2 x 1.2 x 1.2 sized cube.


Extruding this face one short of the full cube size.


Final extrusion so I can work with this face.


Doing the same thing in the Z axis.


Completing the shape. I won't make a full cube here because I can display the bug with just the bottom frame.



Alternative 1: I can fill the empty space with a 0.96 x 0.12 x 0.96 block.


Like so.



I forgot to remove the default texture but whatever. The point is that the gap is clearly visible here. Bad!




Alternative 2: I can instead extrude the inner face to fill the entire bottom.


Like so.


Gap still visible, though.

Vertices are all selected and welded, which removed some 6 vertices.