The sort of engineering only the Germans could accomplish

You're right. One of the most famous politicians of the AfD Björn Höcke can be called a Nazi/Facist without any consequences for you, since it isn't an insult because it's based on true evidence.

It's more complex than that. Simply banning it could make everything worse. First of all, banning a party is something that's very hard. It only happened twice in the history of Germany(except for the banning during the third Reich). Trying to bam them could make everything worse than it currently is, since it would look like the older parties are scared and try to keep their power. This could give the AfD a big boost. Another thing is, that in the case of a failure the AfD could use the fact they weren't banned to promote themselves as "Democrats" that don't want to do anything illegal. In the case it would be banned it would take exactly 2 weeks and you have at least 2 or three parties that do exactly the same and maybe would transform into one big party and we have the exact same problem. More effective would be to stop them from receiving money from the government(every party does that so that they can focus on their political work), or to not give the the possibility to enter the Bundestag(or to hold any other form of political office) as its the case with the NPD.