IMO I think it's useful to avoid getting moderates and people who don't know better caught up in the mess.

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.

However, in past decades, those other networks didn't cause the same level of propagation of misinformation.

I can't teach your kids to identify misinformation against your will and theirs.

That wikipedia link for the backfire effect directly mentions failure to reproduce the findings.

I will assume that's true, or you won't find this reply very convincing.

Of course this is undoubtedly true. However, deleting the information creates a Streisand effect and a much stronger belief perseverance and backfire effect compared to annotating the information with a counter-argument.

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.

You clearly have a strong belief that it won't be helpful, so I won't try to argue with you.