Not to mention any lead from non-FMJ or TMJ bullets. Lead WILL get vaporized by the charge during firing and I'm sure some sticks back to the brass. I only use TMJ/plated bullets, so if it was only my brass I wouldn't be as worried, but I've been scrounging range brass, so who knows what was shot!
I just read here or other forum from one guy who got lead poisoning and was testing to see where it came from. His reloading area testes fine. It was only when he tested the tumbler did he find significant lead contamination. Other readings say that lead does not penetrate the skin easily, so I'd rather deal with it in liquid form, than breathing in the dust. I'm sure I'll get lazy at some point and just stop washing, but for now I'd rather stay safe. Plus my kids go in the garage where I run the tumbler.
It's not that hard to wash. A few swishes, quick soak, and then an hour in the oven on LOW (150-170) and they're good to go. You could probably just reload at that point, but I go ahead and tumble. More for the final polish than anything. If you don't screw up and leave them in overnite like I did, you should get the tarnishing.