I found that no amount of tumbling (as in leave it in the tumbler 24x7 for a week) removes anything at all from either the primer pocket or the inside of the case, so, I don't tumble at all anymore.
From time to time I do deprime and size then clean in the ultrasonic tank with a citric acid cleaner (about 8 minutes). I then have to rinse and dry, and that process can cause problems of its own (failure to completely dry can mean wet primers, failure to completely rinse can mean corroded cases, etc). The advantage for me is that the inside of the cases and more important to me, the primer pockets, are spotless, shiny and like new brass.
After that agonizing process is over, I then hand select a few hundred cases for personal defense loads, taking a little extra care to get cases with little or no burrs on the case rim and the best case necks.
I also reload uncleaned cases several times if I'm not concerned about poor primer seating--I shoot almost exclusively indoors so brass exterior is generally very clean.
Clean case
interior is nice for visual inspection of the case just after the powder station on the press--I have a flex-mounted light that shines right down in there, and I can spot a bad charge if I'm paying attention. Tumbled brass is, for me, just about the worst possible situation for this because I've always used rouge-based media, and that stuff turns case interiors into the darkest black hole in the universe. I'm sure other media is somewhat better, but it hasn't worked out for me and my way of doing stuff. That's all.
This is 40SW brass right out of the ultrasonic tank:
That's clean.