I say this because I recently saw some users deleting thousands of their post concerned about their privacy.
Some alternative for this would be nice
This is a public discussion forum. If you're worried about your privacy you shouldn't be posting things that can identify you but if you're that concerned about privacy you shouldn't be posting them to a message board hidden or not because they can be intercepted in a number or ways. If you want to do this either hold things in a draft, message them to yourself or even better just keep a digital notepad with this stuff written down but I don't see the point of having it as a forum feature.
Looks at this member who deleted almost all of his posts: BobLawblaw
https://bitcointalksearch.org/topic/this-member-has-weird-stats-5263490
Yes people can still find posts in LoyceV archives or archived with wayback machine but it is not exactly the same.
If someone is privacy oriented, then they should not create any username that links them, should use tor browser when visiting the forum and shouldn't post any sensitive personal information in the forum. It's that simple.
All the stuff about the amount of information the forum retains and how best one can practice privacy in the forum can be got here: https://bitcointalk.org/privacy.php
Moderators can hide post and move them right?
But regardless of whether we allowed this feature or not some users would still decide at later date that they might now want they posted to be available. People are free to delete them but people should be careful whatever they post online as once it's out there it's likely there forever as some site or another will likely be indexing or archiving it.