I find it very hard to belive that tumbling brass would reduce enough material to ever make a differance. My 218 BEE brass is about .008-.009" thick at the case mouth. I have shot it several times and tumbled it several times and I see no ill effect on case wall thickness or reduced neck tension from deminished brass. I have seen the brass work hardened to the point of neck splits, but that is another topic all together.
Even with walnut shell media, I've never seen brass removed by tumbling, and I go through a lot of brass. Walnut media is softer than the brass, and therefore can't cause case erosion. Brass cases should be cleaned before reloading, to protect the reloading dies from getting embedded with grit, which ruins the dies, and also the next cases you size with that die. Polishing brass is not really necessary, that's more of a workmanship type procedure, but you do want clean cases to reload. Work hardening is probably the number one killer of brass cases, and that's difficult to get around with handgun cases because at least the case mouth should be resized to hold bullets in firmly. Chemical cleaning of cases is just fine. Just don't use anything with ammonia in it.
