There's no simple solution to this problem but note that the problem is not so much that we're "bored of disputation" is that we're "overwhelmed with disputation".
It's always the same issues: making a bold, unsubstantiated, potentially inflammatory claim like "Vitamin E is the future of medicine and you should all take supplements, don't listen to what big pharma says!" takes only 10 seconds. Debunking the claim however would require some time and effort, mainly because proving a negative is always more time consuming that making a wild claim.
That's not the same as saying "free speech leads to truth". It's saying "truth cannot exist without free speech". The fact that some people are "bored of disputation" is not a good sign.