Open debate and public disagreement is a healthy vital tool of progress when the claims and argument are made in good faith. When both parties believe their position is true and is good for the world, and their arguments for it are genuine, then I think it slows progress to cancel them.
But if you assume all arguments are in good faith, then you leave the public sphere ripe for exploitation. This is what white surpremacists and others have clicked to recently. A bad actor can exploit a presumption of good faith to add legitimacy to their position. "Look, famous person X rebutted me. My claim must be at least significant enough to be worth rebutting." Or they can use it to make the other party look bad by sea-lioning. "I am merely politely asking questions. Why are you so angry? Aren't you able to control your feelings?"
"Cancel culture" and deplatforming are important tools to defend against these bad faith exploitive uses of public communication.
The challenge is that as we get increasingly polarized and tribal and as the bad faith actors get more savvy, everything starts to look like a bad faith argument. And at some point, people start concluding that the only foolproof algorithm for determining if an argument is in bad faith is "does it disagree with me?" And then you start seeing the banhammer swung freely.
That in turn increases polarization and tribalism because good faith dissenters, people with middle ground positions, and people who aren't sure where they stand self-censor to avoid taking friendly fire.
It is a very nasty feedback loop we're in, exacerbated by the already bad feedback loops of social media AIs being trained to show us content we already agree with.