The model of elementary particles is analagous to the periodic table, which is organized not only beautifully, but also functionally. The typical model for the elementary particles that pops up everywhere (a), while compact, leaves out almost half of the particles, (antiparticles), and personally I feel like it's unorganized and doesn't convey the information clearly (spin, charge, mass). Is there a reason this is what's used, instead of something more complete and organized? (like this (b))
What you chart depends on what you want to emphasize.
The periodic table is for chemistry. It's not organized by atomic number, or atomic weight (mass); it's organized by electron shell properties.
Similarly, the usual SM fermion chart emphasizes interactions via:
- The weak doublets, because they're key to electroweak physics
- The quark/lepton distinction, to show who responds to QCD
- And the generation structure, for the same reason the periodic table groups columns: These are pretty much the same under interactions.
But by the time this came along, particle/antiparticle didn't need to be shown because it was assumed: Much like the periodic table assumes you know that hydrogen, deuterium and tritium are really all (for chemical purposes) in the H box in the table.
Nor is there a real need to emphasize the electrical charge, because (a) it's subsumed in electroweak and (b) it's just along the rows anyway, if we wanted to label that.
The short answer is "because it actually makes sense", largely due to the recently deceased Gell-Mann, who, within a bracket of 4 (arguably 10) years served as a combined Mendeleev and Moseley for elementary particles, that is, he both classified them and understood the reason/structure underlying that very classification.
The actual particles'analog of Mendeleev's table is more complex than the WP version you are displaying, and the PDG classroom chart gives you a whiff of the multidimensionality issues involved. (It is, still, quite superior to the WP one in listing actual neutrino mass eigenstates $\nu_L,\nu_M,\nu_H$ rather than "flavor basis" linear combinations of them whose " lepton flavor" is actually primed for violation — the very moment they are born! Lepton flavor is an oblique quantification of the slowness of neutrino oscillations. This is a ritual instance of conceptual recalcitrance of "science educators" yet to be overcome...)
The logic of the WP chart you are asking about, however, is, in fact, served quite well by it. Bosons (force carriers) are split starkly from fermions (matter), color is utilized to contradistinguish the four most important groupings: hadronic constituents; leptons;gauge bosons; the Higgs. Columns are demarcating generations (which in a loose sense rank masses of similar particles). And it is compact, encoding visually what most particle physicists carry in their head at present.
Could one devise a superior logical sinecure? Perhaps, but overemphasizing charge, given the conceptual engine of the SM, weak isospin, is potentially misleading. In the census, one rarely tabulates individuals on the basis of their hair color.