It would be much easier to say "let's ban the dissemination of the idea that it was faked" than to say, let's go out there and show all those deniers and people who listen to them and show them the facts.
We know it's difficult to change the minds of people who hold steadfast views like these.
But the side-effect of something like this is pretty dire. You get what the PLA and the CCP exercise in China. There is the official, sanctioned version, which because it is shaped by body can take any shape the controllers want.
So instead of random people making up facts, you can have a center of power making up faked facts --and you can't dispute it, since they provide the official version of things.
What other information should the government deem fake? And where should this Ministry of Truth be headquartered?
This is so self referential it should be called Brandolini's paradox.
I'm not really sure we can blame them. The atrocities that Nazis have commited are still in living memory, there are still bullet holes in walls, whole villages are destroyed and the remains are still there... and hate over death of family members is an extremely strong emotion.
The post war german generations were not teached that they are guilty, but that they do carry responsibility for being aware of how easily facism and dehumanisation happens and escalates, and of keeping the memory of such evil present.
And yes, this includes the responsibility of being aware that similar things may happen again, clearly detecting extremism by the root, calling it out and hopefully averting it. Probably every country in the world should put such emphasis in their history lessons, but nobody else ever really will for obvious reasons.
So this kind of became a responsibility of the people born in modern germany. This is why it is one possible Abitur topic in politics, history and german lessons, why it is one element of the curriculum in (3 to 4)+2 different middle school years + Abitur (saxony speaking) and why there are high school visits to concentration camps.
As someone whose school system has provided them with some insight on how this all happened I see the US absolutist view on free speech when it is about outright lies like Holocaust denial as a bit dangerous. Preventing deluted individuals from spreading a life-threatening lie is not censorship. I see that the US view is coming from a very humanist view here, but tolerance needs to have limits set by basic human rights values, otherwise it will be destroyed by itself sooner or later.
The approach to "educate the deniers" is indicating to them and the listeners that you are taking them and their delusions seriously, and dissiminate them in the process. In the current debates about e.g. evolution you clearly see what happens in wider society if you talk to the 1% "skeptics".
There is a ban but it doesn't mean the german government goes out of it's way to remove any piece of such material before it even hits the internet.
It's largely post-factum, when the piece is already on the internet and spread elsewhere when the original author of the information is punished.
Where I live, I'm vastly outnumbered by people who have vastly different values than me. Their party is in control now. Pretty scary to think they could shut off my voice at whim, or worse.
It's the "let's burn books" mindset, which is just a bad tactic. Misinformation in the modern(or any) age can't be fought that way. The internet is good at amplifying that which people seek to censor. I hope we can agree this is good for positive ideas, but the mechanism employed doesn't care how "good" you find the idea.
And to be entirely clear: I think the subject matter at hand is abhorrent. Fascism feeds on censorship. It doesn't hurt that side, it helps them control the narrative.
Nobody wanted the Nazis to return. That goal was more important than any other. The Soviets accomplished it through pogroms. The west was more subtle.