This is an opening that's getting popular, which I like, but people haven't really talked about it yet.
The idea: Open Church/Church. Hope you draw a Church turn 3. Set aside a bunch of Coppers on turn 3, buying nothing, then buy a $5 cost on turn 4. If you draw a Church turn 3, you are almost 100% guaranteed to have 5 Coppers on turn 4, and will usually be able to trash an Estate as well.
It's good when: there is a $5 cost you'd really like in your deck by the end of the 2nd shuffle.
It's less good when: there is some other $3 or $4 cost you also really want early. Your expectation should be that you spend your 2nd shuffle trashing 1 Estate and buying a $5 cost. If there's an alternative card that will do more than 1 Estate trash while giving you good $5 cost odds, it'll be better.
The deceptively powerful parts: If you draw a Church turn 4, you can set aside any extra cards you don't need and they'll miss the shuffle, letting you draw and play your $5 cost faster.
Let's show a few scenarios to show how this thinner shuffle can be good.
If you draw one Church turn 3 and one Church turn 4, it's not too rare to trash an Estate, then set aside 2 cards on your turn 4 (Estate + Copper). That gives a 9 card shuffle (1 Church, the $5 cost, 1 Estate, 6 Copper, with 1 Estate trashed, and Church + Estate + Copper all set aside). If you then draw the $5 cost in your first hand of the 9 card shuffle, it'll get reshuffled at the end of that turn, you get small chances of high-rolling redrawing the $5 cost.
If you draw both Churches turn 3, you set aside your entire hand, then get 2 trashes and a $5 cost.
If you draw both Churches turn 4, you will likely miss $5. However, you can set aside your entire turn 4 hand, and your shuffle will be 6 cards (your turn 3 hand + turn 3 buy, with 2 Churches and your entire turn 4 hand set aside). You then will almost 100% hit $5 on turn 5, and that $5 cost will get shuffled in right away thanks to how thin your deck is.
In short: the open is best if you draw a Church turn 3, which is pretty common given you opened 2 Churches. If you don't do that, but draw a Church turn 4, it isn't that bad of a fail case. And if you don't draw any Churches on turn 3 or turn 4, then you sombrero-ed, which is very uncommon, and can't be played around anyways.