Yeahhh shuffling!
I think the reason pile "shuffling" became popular is a Darwinian trend where people who do it in MtG or other TCGs tend to win more and have more satisfaction because it essentially stacks your deck. After an MtG game is finished, your lands and nonland cards are clumped together. The best case scenario in MtG is to get an even distribution of lands and nonlands. So when you pile shuffle after a game of MtG is complete, your deck goes from clumpier than true random to less clumpy than true random and you gain a distinct advantage. Even if you supplement this with truly random shuffling techniques, you've created a starting point that's really good such that if your riffle or mash shuffles fail to completely randomize, it errs on the side of advantage.
Whenever I play MtG I always do "cheat" and pile shuffle before I perform true random shuffles. There's no rule against it. MtG's rules dictate that if you're not satisfied with how your opponent shuffled, you can take their deck and shuffle it as much as you like, so if I don't riffle or mash enough to undo the advantage I created by the shuffle, it's my opponent's responsibilty (and capability) to shuffle additionally until it's very close to true random. That said I do mash shuffle my own deck until I feel comfortable with, I don't deliberately undershuffle. I just want accidental undershuffles to work in my favor.
If I see my opponent pile shuffle but don't see him riffle or mash shuffle many times, I exercise my right and mash shuffle his deck to make sure he's close to true random.
In Dominion, the effect of pile shuffling is gonna vary. I tend to put my Smithies and villages together to count actions more easily, so if I pile shuffled I would be wrecking myself. In other situations it might help you. In a friendly game of Dominion I think you should probably not pile shuffle at all because it's not randomization and you're just wasting everyone's time. If you are playing with someone who is new to card games and has trouble randomizing their decks and is having an unfun time from curse clumps or something, then letting him pile shuffle would be ok. But for the most part other players shouldn't be waiting on you for you to do something that's not randomization. If everyone doesn't pile shuffle, no one has an advantage.
I find it interesting to hear/realize that pile shuffling is reversible, because that could have a crazy application for MtG: if someone plays a game, pile shuffles, then riffle/mash shuffles only one or two times, then when the other opponent takes their right to shuffle the deck, they could perform a procedure that reverses the pile shuffle, then perform no other randomization. The player who underrandomized would then have a very high likelihood of getting clumpy draws.
Shuffling is kind of a chore. I hope Donald does the chips in a bag thing when he makes a Dominion spinoff (with due credit of course)