I agree that tumbling brass is one of the most discussed aspects of reloading and I agree that it is possibly the least important part as well.
When I first started reloading and for several years, I didn't clean my brass in any way. I just loaded it. Now 30 years later I still do that on a regular basis. But, today, this usually just happens because I am loading and I have some brass that I just shot, and I figure, hey as long as I am rolling on this project I might as well load all the empty brass I have: so I just load the dirty brass. The vast majority of it was cleaned but the last 50 or 100 were just shot and loaded dirty (I typically load a thousand or two at a time in handgun cartridges and then shoot that until I am running low, then load everything I have at once).
I have nothing against people who really spend the time to polish their brass and clean it super clean. It looks nice. It gives you a feeling of satisfaction. I just question whether it is really nessessary.
I have tried dryer sheets to keep down the dust, but typically I just use some strips of paper towel. To me, this isn't about keeping dust down in the room or breathing dust, it is about not having dusty cases. The best way to avoid this is to regularly change your media. As the tumbler tumbles, the grains of media grind down producing dust. If you keep your media too long, the cases come out covered in dust. This dust annoyed me to the point that now I mostly use an ultrasonic cleaner. Lately I have been going back and forth trying to see which is easier to get minimally clean cases with the least effort and time. The obvious problem with using an ultrasonic cleaner is that now the brass has to dry.