Let's dissect these mantras so as to elicit some deserved eye-rolling
To some extent, isn't part of the problem what you think is the "invisible hand" of the "marketplace of ideas"?
If you're all-in on "social pressure is the invisible hand", then you're likely to believe that ostracism (or even censorship) of the opponents is the winning strategy. You're likely to be more concerned about the unequalness of the playing field causing a chilling effect on marginalized people, than you are about the traditional legal arguments protecting freedom of speech (including "hate speech" or "dehumanizing speech"). You would also be likely to believe that your opponent has come to a similar conclusion and be concerned that a denial of a "right to exist" is fundamentally your opponent's goal. Honestly, I blame literally everything on blank-slatism and social constructionism, so I genuinely assume that most people who are against debate and free speech think along this line, but am probably provably wrong.
If you're all-in on a "free speech is the invisible hand" side, you're likely to get strawmanned by any of these three. Debate isn't magic that solves everything, but it's incredibly powerful. Whether its power comes from public mockery of bad ideas, moral high ground, awareness of serious problems, FACTS and LOGIC, persuasion and mobilzation, contact with and sympathy towards differing groups, or some other source... explaining the exact mechanism by which debate will solve the problem is not necessary because the market will figure it out (mostly). Obviously, not knowing the exact mechanism for the specific situation can lead to a perception of it as "the naive position that if only people had access to the right facts and information — delivered via civil discussion, of course — Bad People would change their minds, becoming Good People". Also, there's no real reason that a specific instance will be recognized as good at all, but somehow each individual twitter shitpost will be work toward a public interest.
If we buy into this dichotomy I asserted without any real evidence, I think that the "free speech is the invisible hand" people are right, but at an important strategic disadvantage. It's very easy for anti-debaters to cite specific examples of where they were right and the exact mechanism for them being right, and much harder for debaters to prove that allowing debate completely at will is good for society as a whole. We, in general, know that people don't particularly care about facts in the body of a post as much as moral claims in the headline. A bad popular idea is often 10 times stronger than a little-known right one. We know from people like Christian Picciolini and Daryl Davis that conversations can deradicalize white nationalists, but there's a lot of heat on Twitter and YouTube to deplatform the "Alternative Influence Network" who are apparently radicalising the kids because they interviewed Milo Yiannopolis and Candace Owens. Honestly, I can't comprehend someone being more in favor of Owens after hearing her speak, but I'm proven wrong every single time.