Wow, this is an impressive discussion. How about possible solutions or a temporary fix?
I happen to have two gmail accounts set up on the same Mac (10.9), neither of them set to "all mail" (both with IMAP path fix set to "IMAP").
Interestingly, one is affected by the reappearance bug after deleting the message, whereas the other one works totally well with Mavericks, as it did before with ML. That doesn't indicate to me that this is a total desaster from the side of Apple or Mavericks. It looks like there is some minor assigment problem that might be easily fixable once figured out.
Also, a simple solution that works perfectly well for me has been posted here but it seems to have gone widely ignored.
Just use "option backspace" for now and the selected message is deleted permanently and doesn't reappaear any more (after quitting, chnaging accounts or whatever).
That's it. There was no need to change any other settings with this one. I have tried this for several days now.
Full credit goes to
RCSman
Re: Mavericks Mail App and Gmail folders