Philosophy
Have you been in a cave for the past decade? It doesn't matter if someone proves something is stupid, the world doesn't run on intelligence and logic.
We literally let the Nazis talk and now they're in control!
In a world of rampant anti-intellectual, disinformation, and rising fascist movements, you're suggesting we should allow dangerous ideologies to be spread unchecked out of some naive belief that people will suddenly, after years of this not being the case, disregard them due to finding them stupid?
Talk about proving how stupid you are.
For succinctness I'll interpret "stupid" = "immoral and/or false".
This assumes your typical person naturally discards a stupid discourse, once you show it's stupid. I don't think they do; instead they'll discard a discourse that conflicts with their world view, and is not emotionally engaging enough to replace it.
In the light of that, "let the Nazi talk" sounds like a notoriously bad idea. Specially when the Nazi in question are highly rhetorical, i.e. make their stupidity highly emotionally engaging.
A better approach is to address the core claims of the Nazi discourse, in absence of their rhetoric, showing why they're stupid (and cringe). That's basically what a lot of people already do.

Who is this elegant nazi puncher?
This would be Indiana Jones disguised as the guy checking the passengers tickets in a blimp, protecting his dad, sitting behind the nazi. It's from The Last Crusade.
Fly? Yes.
Land? No.
That's Indiana Jones! That Nazi didn't have his ticket
He didn’t have his ticket
No ticket. 🤨
We already fucking know, tho. They need to STFU.
Well, the problem is, there are more stupid people than smart ones. And they vote, too. Would the world be a better place without stupid people? Imagine a world without stupid people. It would be amazing.
Hey, look, fascist and antidemocratic rhetoric.