You have hit on the exact superficiality that drives people into supersymmetry theories. There is nothing fundamentally absolute about a 2-ODE governing the dynamical evolution of a ``particle''. Square your Dirac equation, and you get a 2-ODE (KG), but the former is still more illuminating and contains as much information as the latter. In fact, the requirement of spin and dimensionality (N=4, simplest realizable case) follows naturally when you adopt a critical perspective towards a 2-ODE (it gave <PERSON>, probability densities that weren't positive definite and that made no physical sense, unless you start inventing new conjectures (e.g. hole theory)). (You know these stories, don't you. Otherwise read <PERSON>, <PERSON> - that won't be too many details, but just enough).
let us take the simplest N=4 case (that's the lowest dimension in which you can realize that group structure. 855
But of course, higher ones are possible.) We can make `physical' sense of this dimensionality by recognizing that the four components of the bi-spinor carry information regarding (spin up, spin down)*(positive energy, negative energy) parts. But again that dimensionality was forced by the group structure and is NOT a matter of any fundamental distinction between a particle with spin and a spinless particle. Square the operator part of the Dirac equation, and you will get a 2-ODE for each of these components.
So, this entire formulation creates this misleading impression that dimensionality of space creates any fundamental distinction between fermions and bosons. How this gets treated in SUSY is a tad too detailed to be mentioned here (plus, it will kill the fun, when you eventually learn about it from reading a textbook). I genuinely recommend <PERSON> SUSY book and would only leave you with a teaser - not just that there is no absolute distinction b/w fermions and bosons, the spectrum is much richer; ever heard of `anyons'? That's OK, you'll find out in due course of time. Happy leaning :)
PS - Like every conscientious physicist, I leave you with a word of WARNING. SUSY is a beautiful theory, could be a great step in the right direction if it is proved correct. BUT DON'T TREAT IT AS A BIBLE, UNTIL THERE IS ANY EXPERIMENTAL EVIDENCE IN FAVOR OF IT, no matter how beautiful it may be. 855