To me it looks like the periodic table. There's an underlying set of levers in terms of quantum characteristics of fields, but not all settings of these levers are stable. This is just like how only atoms with certain combos of protons and neutrons and electrons are neutral and stable.

If you look at histogram plots of protons, neutrons, and stability, it's not a perfectly idealized form. It's a rocky plot. This emerges from the quantized nature of reality.

So a periodic table of particles (fields) that looks kind of weird and ad-hoc to us is the expected result.

What we don't yet fully understand is really two things as far as I know. First, we know less about why these particular values are special. For the periodic table we actually understand this pretty well. Second, we do not know if there are other islands of stability or particles-fields we cannot see (e.g. WIMPS). For the periodic table we are pretty sure there are no large islands of stability at higher weights. Not 100% sure, but if they do exist there's probably only a few exotic mega-atoms that could be stable, not many.