Looks like I'm in the minority here.
I wet/ss tumble my brass after every firing. Bring the empties home, deprime, and tumble in tap water and a couple drops of dawn. My main reasons for doing this are keeping my dies and equipment clean and keeping the brass and primer pockets clean. I think there is something to be said about keeping the inside of cases and primer pockets clean and uniform. Carbon deposits eventually build up and change internal volumes.
For drying I just roll them out flat on a towel. At some point I'll roll them around a bit. Then when moving them back into boxes I shake/tap them to make sure there is no media left in the cases. I average like 5 pins inside cases per 100 at this point. I generally put them in ammo boxes neck down so anything left will drain. I shake the boxes around a little sometimes too to make sure the brass is dry, clean, and empty.
After typing this, it makes it seem like a lot of shit. Realistically, it takes me maybe 15 minutes per 100 cases for all the hands on steps. Tumble time depends on how many and how dirty they are. 1-3 hours, usually. I let them dry on the towel overnight.
BTW, I've got an US cleaner too. That's reserved for gun parts.