#1.
As content matures, its sorting will change. If we move something once we discover that it's inappropriate for the board it was posted to, that has an impact on the content in question, but also other content in the board it's moved to.
While this statement is basically fluff, I understand what you're getting at. Threads being moved are affected differently by the sorting conventions present in each individual board.
That being said, is there any particular reason you can't move just the content of the thread rather than the vote totals and how they affect sorting? Threads should never be getting to the point where they are well-established with high vote totals and comment density before they are deleted, and I have trouble seeing an instance where moving a thread with 5-10 comments from a different board to the one that's relevant would be a particularly bad thing.
#2.
Since we started deleting stuff instead of moving it
When was moving the default rather than content eradication?
There's evidence to suggest that boards users spend more time thinking about where they post content before they do so.
What metrics are being used to support this evidence? If this conclusion is primarily based on how often users post content in the wrong location, we're kind of just looking at correlation and ignoring potential tangential causes. For example, if content is not properly explained when deleted, users may just not even bother continuing to add novel value to the platform. This might technically mean the user posts in incorrect locations less often, but it may potentially be stifling.
If it didn't matter where you posted crap because the mods would fix it, I believe we'd be digging ourselves a hole that would hurt everyone long term.
One would assume this is the case, but historically (through forums that allow moving) it just doesn't happen. With properly scaled punishments and effective guidance, it's pretty unlikely for someone to repeat a mistake like misposting. From a psychological standpoint, people don't generally work on something with the intent of making a mistake. If they are intentionally making mistakes, they probably deserve a punishment that differs from those that are clearly just misguided.
Using your fishing analogy, I would honestly consider moving to be like teaching a group of people to fish. Moving a thread with a clear public moderation message not only specifically addresses the OP, but it's also something other people can view and learn from. Deletion would be more like handing a man a fishing rod and telling him how not to catch a fish, and I just don't think that's as effective a learning tool.
#3.
Returning to a board and not seeing the content you posted is jarring.
Agreed. It's tough to see that something has been removed, and I'm glad this is being improved. I actually have a quick question: When a reply (not a thread) is deleted, does the moderation message show the actual content yet or does it just link the user to a comment that just says "Deleted"?
I'm more than happy to go back and forth on this.
I sincerely hope this is the case, because historically this has been difficult.
Edit: Over a week later, no response. I understand you're a busy man, but this is a consistent pattern. If you mention on a thread that you would like to have a discussion or go back and forth, it's important to follow through on that statement.