moving a forum game that's being taken very seriously to Memes and Games
If it's a forum game, it should fit in Memes and Games. It doesn't matter if it's taken seriously, it's still a forum game.
A possible forever back and forth movement between champ&skins and LGB
This would happen regardless of whether it was moved from somewhere else. Besides, to my knowledge it's actually intended for the Champions & Skins section to encompass anything related to champions/skins, including live balance.
moving a good OP that was killed by unproductive "pitchfork and torch" discussion to an appropriate Board that isn't used to that
In my opinion, if it was already killed by unproductive discussion it's...dead. There's no need to move a dead thread.
Tight leash to be loosened later kind of mentality
There's a distinct difference between a tight leash mentality and a nullification of discussion mentality. From my perspective, deleting threads for being in the wrong place is a deterrent to discussion. If the tech allows it, it makes no real sense to not just move it so the OP isn't forced to recreate the thread & commenters aren't ignored.
Deleting and not moving thinking could work if every deleted post was deleted before much discussion is made and a transcript of the deleted post is provided (which I believe it being done actually, correct me if I'm wrong)
I'm not sure how this is being done currently, but from what I've gathered it informs the OP and not people that posted on the thread or were interested in it.
I know I'm beating a dead horse/preaching to the choir/insert cliche here, but generally speaking I'm just a bit concerned with the absolutism in deleting > moving. Moving a thread is a dynamic thing; in the right system, all participants in a given thread are notified of the move and are able to migrate appropriately. A deletion is an absolute; if a thread is completely gone from the Boards there is no way to continue discussion short of the OP remaking it.