Why do no known atoms have electrons in the g or h subshells?
Well, the first available sub-shell for "g" electrons would be 5g (i.e., 1s, 2p, 3d, 4f, so 5g). Based on current trends, we'd need row 8 of the periodic table. We just haven't found those elements yet.

Let's look at it this way.


After row 1 (1s electrons only), there are 2 rows of the s and p-block elements before "d" opens up with $\ce{3d^1 4s^2}$
After two rows of s- p- and d-block elements, the "f" block opens up with cerium: $\ce{4f^1 5d^1 6s^2}$


So we'd need two more rows of the f-block (i.e., the lanthanides and actinides) and then complete the row.

Right now, we have found element 118, so if we can synthesize a few more, we can open up the "g" block.

Now, there are elements that have g electrons in excited states, so g and h-orbitals are relevant to some chemistry. But the ground-state elements haven't been discovered yet.