Sadly won't be helpful, and may actually make things worse:
* https://en.wikipedia.org/wiki/Belief_perseverance
* https://en.wikipedia.org/wiki/Backfire_effect
* https://www.newyorker.com/magazine/2017/02/27/why-facts-dont...
For people who are already convinced, they're already convinced. Banning the content entirely also doesn't help. People are very good at spreading information, even if you manage to ban all conspiracies from the internet, you have TV, the newspaper, private networks, and just word-of-mouth.
Another good tool would be to teach kids how to identify misinformation. You don't have to worry about belief perseverance when there's no belief yet.
I will assume that's true, or you won't find this reply very convincing.
Between the three options of "delete", "annotate", and "leave untouched", I think the least-bad option is probably the middle one. It's not going to dissuade many people and will only reinforce beliefs for many, but there's not much else that can be done.
The "fake news" part is always disputable on a case by case basis, but the "elite" part is indisputable. A very small number of very wealthy people get to decide the range of opinions that are acceptable, and the deviations that get administrative comments. The mods aren't the auteurs - mods that correct incorrectly will be fired. Close calls rattle up the chain of command until they hit the CEO/Founder, who is often a billionaire, always very wealthy, always of a particular demographic.
And now, the media establishment is doing some kind of re-think, and it turns out that while far from proven, a lab leak (which covers a variety of scenarios, most not involving any kind of "engineered" virus) is a reasonable hypothesis. If that's so, why the capricious banning and warning labels?
We've seen similar situations play out in the past year with masks (at first, they were unnecessary and racist, then absolutely critical, now it's changing again). How about just let people decide for themselves? There will always be some conspiracists on both the left and right, but most people figure this stuff out in a reasonable manner.
That's getting tenuous. Fully 25% of the populace believe "alternative facts" that their Representatives claim are true, but those Representatives cite those very people as the source of truth! It's "citogenesis" in the real world!
I don't see that as a problem.
What about health misinformation that if propagated will kill thousands? How many dead is enough to act?
What if false info about vaccines keeps enough from being vaccinated long enough for a new variant to emerge that infects the previously immune and the net effect is millions die?
I don't think you want to be elected Emperor over this at all its a shittier job than you imagine.
The power to silence will always be abused.