The evidence is that it's only 15%. Free speech doesn't guarantee everyone will have right beliefs. In fact, it's a certainly that in a free speech environment lots of people will have crazy beliefs.
Free speech does, however, guarantee that no one group can control which ideas—crazy or not—can be expressed. And that, in the long run, ensures that there will be space to push back against the crazy and the harmful, which tends to be good for the less powerful.
What would a non-flawed plan look like? One that results in everyone having "correct" beliefs? I'm pretty sure it would be a great deal worse than what we have now.
Nuking social media from orbit would be a good start. Any platform where what content you're shown is primarily driven by an algorithm is very suspect.
Furthermore, in the grand scheme humans beliefs being 'right' or 'wrong', people today probably have far more 'right' beliefs than ever during history. Conspiracy theories and wrong beliefs have been more prevalent in the past than today.
Free speech does, however, guarantee that no one group can control which ideas—crazy or not—can be expressed. And that, in the long run, ensures that there will be space to push back against the crazy and the harmful, which tends to be good for the less powerful.