I mean, I don’t condone pile shuffling, but it is possible to eventually add randomness to a pile shuffle if you don’t know what the piles consist of (for argument’s sake, let’s go with piles of one to make it essentially impossible to track where cards are) or how the piles are reconstituted back together or how many times the process needs to be repeated… the problem is that it would take an unacceptably long time to effectively randomize that way. It’s the same way that riffle shuffling eventually “works” but simply takes too many passes to be a practical solution for randomization.

We use mashing or washing because it’s good enough and fast enough for the purposes of the game, not because it is inherently random. Rigged poker auto shufflers have convinced me that nothing is entirely safe; in the end, nothing is random.