Ok, couple of examples, so it is easier to discuss (didn't think this was such a new/little known idea):

https://8ch.net/log.php?board=n
https://modlog.github.io/#/r/conspiracy

The amount of detail is up for discussion, sure you will not repost child porn to logs, call the police, report IP etc, still a note should be left in logs. Mask IPs by randomly generated ids, or just use account names, mods can be masked to (mod1/mod2...) so people can see when modx goes on a rampage and can complain, admin will know who that is. Plenty of options to consider and not relying on mod remembering to add a note (which is not possible for deleted posts/threads btw)

(and the idea of reposting non-illegal content that was removed to a place like irclogs is good, keeps the thread going (how many OT rants gone missing?), stops link farming as not main site/not a clickable link with markup etc, illegal, sure delete, just leave trace of action taken