I’m going to address the question in two halves: what is the point of moderation overall, and what legal consequences exist when moderation (or the lack thereof) go awry?

Mike Masnick of TechDirt has written extensively about why moderation must exist for any large-scale, publicly-available web platform, most notably in this article describing the “moderation learning curve”. That article goes through the “evolution” of a supposed “anything goes!” platform that is compelled – by economic forces, public sentiment, existing laws on CSAM, and more – to do moderation. But even the very act of drawing a line in the sand will always be objectionable to someone somewhere, so it’ll always be a thankless job. Even harder is applying a moderation policy consistently.

But we’re getting a bit too philosophical. Why does a platform – from the largest like Facebook to the smallest Lemmy community of four people – do moderation? A few answers:

• If stated community’s rules are regularly violated, those rules cease to have any authority
• If users are not comfortable in a community, they will leave
• If posters do not feel welcome to post, they will leave
• If mods don’t take action on illegal or unpermitted content, they themselves might be removed/replaced by the server owner
• If the server owner knowingly hosts illegal content or fails to adequate perform minimal screening, their ISP/CDN might drop them as a customer
• If other platforms or venues exist for removed content, then it’s not really a negative impact on the "marketplace of ideas"
• If moderation removes content that the user-base liked, then those users are free to follow the content to another platform; there are no hostages taken on Lemmy, and radicalization can still form online just like it can form at the local library by reading Wage Labour And Capital

For the legal aspect, I can only write from a USA perspective; IANAL. Broadly speaking, Section 230 of the Communications Decency Act provides that: 1) a web provider that hosts content authored/submitted by another person will not share in any civil liability incurred by that person, and 2) no web provider will have civil liability for their moderation decisions made in good faith. Together, this means only the original author of some defamatory post can be sued for that defamation, not the platform. And if the platform removes that defamatory post as part of moderation, the original author does not have a right to sue the platform. In shorr, this provides a lot of protection from civil lawsuits if they do moderate, or if they don’t. But if they don’t, the practical issues from earlier will still arise.

But federal law imposes additional obligations for web providers, with civil or criminal penalties if not properly dealt with, for specific types of content. That is, content that enables sex trafficking, or CSAM. Sex trafficking was specifically carved out from Section 230, and CSAM is a possession crime: its mere presence on a hard disk, however acquired, is unlawful.

Putting this all together, a Lemmy mod that deletes a post is performing moderation. They might do so because the post is irrelevant to the users or violates some rule. Whether the mods leave the post up or take it down, the broad civil immunity of Section 230 means the platform can’t be sued for it, nor can the post’s author sue the platform. So the post remaining in the modlog does not pose any new legal vulnerability. Rather, removing the post proves the value of having mods, so that other users don’t even have to see it. Post removal intentionally curtails “freedom of reach”.

The exception to leaving content in the modlog is if it might be CSAM or otherwise illegal content. In that case, the mods can scrub it from even the modlog and anywhere on the platform. This complexity is why anyone hosting a Fediverse instance hosting other people’s content is advised to follow guides on how to do so. Here’s another one.

TL;DR: the mods have a job to do, everyone wants a healthy community, and the law has only a small – but exceedingly important – handful of obligations.