I'd say a couple of things.
In a situation where we do have free speech I believe the truth does overall win out in the end; very often it takes a frustratingly long time and often comes too late to repair the damages caused by the lie but I believe that that overall, if you'll excuse the horrendous remark, "the truth does find a way".
I also know that the current lies and propaganda we so often see are an absolute stain on these past decades and I'm also in agreement that something needs to be done. Whatever it is however I'd like to see it built on the free speech principle rather than against it, even if the principal isn't without its flaws.
For example, take fascist propaganda... the lies are effective, and if left unchecked, can convince people to support fascist leaders, who will then block free speech, preventing the truth from winning out.
This is a form of the paradox of tolerance..
Half the US has voted for someone explicitly denying science, half the UK has voted for Brexit, in some areas of Germany 25% vote for people just a few beards short of Nazis, Bolsonaro is still in office. The "average citizen" can not be trusted to vote in their own interest or in the interest of the future generations.
Maybe not, but in a democratic system the right to choose trumps any ideas about what you or some elitist group thinks is best for future generations.
Are you advocating for undemocratic system?
I am a strong advocate for free speech, but I really think it is naive to believe that truth will always win no matter what. History is full of examples where propaganda and lies wins. I am not arguing for censorship, but I am arguing that we need to confront lies and propaganda with more than just platitudes about the truth winning out in the end.
The truth needs advocates.