Why tumble them at all??? If you reload your ammo, it's a good idea to have clean brass so no junk gets in and scratches your reloading dies and the action as well.
If you can't be bothered to clean your brass, buy factory loaded ammo, fire it and dump the brass.
And if you're shooting dirty ammo, I would wonder how well you take care of the rest of your gear. And if you don't reload, my guess is you'll never know the full accuracy potential of your rifle. And, picking tumbeler media out of the flash holes gives you another chance to inspect your brass for defects.