Prove me wrong, I dare you!

Well, the thing about atoms is that they arrange themselves in patterns to create those larger building blocks you speak of. Solar systems move much too slowly, so that by the time they would have arranged themselves into anything resembling the patterns exhibited by atoms, the heat death of the universe would have occurred.

The resemblance you see is orbit, but the major issue with uniting the orbit of atoms and the orbit of planets under one theorem is the scale of the forces at work. Gravity is many orders of magnitudes weaker than electromagnetic force holding electrons in place (and it needs to be that much stronger because of how much faster electrons move relative to their size than planets).

But now we're getting into string theory.

They are. Solar systems make up galaxies, which make up clusters, which make up super clusters, which make up galaxy filaments the largest known structures in the universe. Each one of these recursions make the one before it seem infinitesimally small.