It is very difficult to reconcile democracy with justice for the crime committed by groups in the past. You can't argue away this contradiction; if people have the right to vote, they have the right to vote for groups that in the past committed terrible acts. It's especially difficult when the current groups do NOT intend to commit mass murder, but are guilty only of softpedaling past crimes and wanting to enact policies that fall far short of what their predecessors did.
If you ban a party that calls itself Communist, its members will regroup and call themselves Democratic Socialists, and present themselves to the voters. Nazis were banned after World War II, so their followers created Populist Parties or Nationalist Parties which did not say "we're going to kill all the Jews" (since that problem was "solved" anyway) but did put forth nationalist, anti-capitalist, anti-immigrant rhetoric. You can't keep human nature down. It's just not that easy.
Where would you even find trained judges in post-war Germany to try Nazis, when every judge has been a Nazi? A very high percentage of judges, years after the war, had been party members. Being trained in the law in the 1930s and 1940s meant being entwined with the Nazi state. These obstacles are real and enormous.