Aside from defending free expression as a matter of principal, yes it actually does work over time.
Except during a brief, half-baked spell of McCarthyist schizophrenia in the 50s, the United States, during the whole course of its massive cold war with the USSR, never saw fit to ban support for communism, the publication of communist literature, open talk in support of communism, or even the existence of an actual communist party inside its borders (thanks 1st amendment). Despite this, said ideology simply having to compete in the marketplace of ideas and practical reality, slowly turned into more of a running joke than any real threat in any meaningful sense to U.S society.
Bear in mind the obvious too: once you create the legal right to legally repress insidious ideas, it's a very small leap for successive administrations to also start banning "insidious" ideas, meaning anything they happen to not like out of some self-serving convenience. In the west, there has been, since 2016 in particular, an intermittent fever of force-fed fears about the so-called dangers of misinformation, one promoted by media and politicians both, only for that very same idea to be used by one robust list of real authoritarians specifically to crush disagreement with their particular variants of nonsense, mendacity and propaganda.