If permabanned users are just actually told that they're banned for copy and pastes then 98% of them probably won't bother creating another account to ask why (though I'm sure some will still do so to try futilely protest and whatnot).
I still like the idea of having a child board, but the above suggestion would probably help. It would be even better if banned members were given an example of what they copy/pasted, which I think is usually provided when someone reports a plagiarized post to a moderator. That's probably asking way too much if the current system for mods issuing bans is as clunky as you say (and I believe you), but showing someone exactly what they plagiarized would likely cut down on ban appeal threads even more--or at least we wouldn't get all the stupid "what did I do wrong?" posts. Those are unnecessary and waste people's time, because invariably someone goes digging to come up with an example.
But even if a reason and an example were provided in the ban message, I would bet money that these people are still going to keep making Meta threads asking for mercy, giving excuses, and lying through their teeth about how their dog stole their laptop and somehow managed to copy someone else's content. That's why I think the child board solution is a better one, and I disagree that Meta would be empty without ban appeal threads--if anything, it'd be easier to find actual discussion threads.
Best solution should be the Reason of the ban in the Ban Message self !
That's not the best solution, but as I said I do think the reason should be provided in the message. It's a start.
Maybe the best thing would be a pinned Topic in Meta with maybe Titel " Complaints about Banned Accounts "
That was suggested before, and the main problem with it is that most banned members won't read it or will still create an appeal thread begging for mercy, complaining about the ban, or whatever else. I don't think a pinned topic would help at all.