I use a universal decapping die, so there's no issue of getting my 'real' dies full of dirt. I run dirty cases through that, then into the tumbler and then back to the bench for reloading.
Actually, tumbling is hardly necessary. A wipe-down with a cloth soaked in lighter fluid is enough and, unless you are going for super accuracy, cleaning the inside of cases is pointless. There are cheap tools for cleaning 3D cr*p out of primer pockets and I used them for years.
I still use a tumbler, however. Among other things, it makes it easier to notice cracked cases, incipient head separations and so forth. I recently switched to a much finer ground walnut shell, which doesn't seem to plug the flash holes (and yes, "the very definition of tedious" is a good way of describing that problem). I suspect I will be switching to stainless steel pins eventually, but there are other priorities for my wallet right now.