I can't believe what I found, but I've come across an egregious example of abuse of self-moderation on this forum. The user with username "Excimer" has not only deleted some or all replies they disliked, but also completely changed the topic of threads and even moved them to different location. Here is the table of proof.
There are no rules to self-moderated threads. The OP has no restriction to which reply to delete, If the OP chooses to move their thread to a different location it is left for moderators of those boards to decide if the thread belongs to that board or not.
Here is a thread from themos about self-moderated posts, I think this will clear all doubts and arguments.
In most sections, you now have the option of marking topics self-moderated when creating them. In self-moderated topics, the OP can delete replies. The option for enabling this is under "additional options". Topics cannot be converted to self-moderated topics after creation.
There are no rules to self-moderation. In self-moderated threads, replies belong to the OP. In other threads, replies belong to the respondents individually. Think carefully about whether you want to reply to a self-moderated topic, as your post may not be given due respect.