As a non-expert on Weimar politics, I think part of the reason the SPD was chosen is that they are large enough to be pretty influential and relevant to things while also being diverse enough to feasibly take differing courses. I think many other parties are so defined by their political stances that it would be less of a historical simulator and more of a what if:
"What if the Communists weren't communist*
"What if the Nazis weren't Nazis"
*What if the Catholic party stops advocating for Catholic concerns"