We can look to German society for an alternative balance on the principles of free speech and Nazism. Germany isn't doing too bad as a society in terms of individual liberty and prosperity. One might argue they're better governed than any particular state in the US, or the US overall.
Germans also understand Nazis better than the US and they decided their democracy doesn't need it.
Modern Germany has its fair share of problems with how the state can define permitted speech and use it to censor selectively. Since the legacy of the Nazi era is still there, along with the legacy of the Stasi era, German society and government are generally careful to not go overboard on certain things, but this would apply either way. Does anyone really think that the only thing stopping the resurgence of Nazism is a law prohibiting swastikas and certain kinds of speech? No, it's a general social tendency towards avoiding strong authoritarian trends, based on some of the worst historical experience possible.
In essence, these laws don't really "help" anyhow in terms of stopping any serious movement toward extremism, while on the other hand sometimes selectively being used to censor in completely nonsensical ways.
Also worth noting, historically, it was exactly a fear of letting deeply hated ideological enemies of the country's conservative elements that caused the Weimar conservatives to make justifications for censoring ideologically opposed viewpoints and "protecting the nation" against their definition of treason through laws that created loopholes for authoritarian control. This very same perceived need led them to an alliance with the Nazis and the formation of the Hitler cabinet of 1933, after which the much more extreme Hitler used the same legal loopholes -so easily exploitable by serious authoritarians- to completely destroy the Weimar Republic and all of its existing political, social and individual freedoms.
The so-called paradox of tolerance is bullshit. It was specifically intolerance and legal mechanisms for its expression against supposedly extreme viewpoints, that destroyed Weimar Germany and led to Nazi Germany. I have yet to see a country where too much free expression leads to more repression. The exact opposite is the case everywhere you look. Politicians and ideologues establish "reasonable" limits on extremist speech and later expand those ever more censoriously as they redefine extremism or treason to include anything that supposedly divides the nation, ie: goes against their views of a unified political system.
Germans also understand Nazis better than the US and they decided their democracy doesn't need it.