Not always, but not an insignificant amount of the time.
Maybe that's interesting to whichever person thinks it's "an insignificant amount of the time". Which by the way isn't me -- I've only noted that most of the time it won't make a difference, and ventured a quick guess at less than 20% of the time.
I was pointing out that nobody is saying that the "additional card is always going to be that bit of additional treasure you were just dying to play with Storyteller", as you stated. In fact, I specifically said that it's not always going to happen:
Sure, the card isn't going to draw you more if you already had 3 copies of the highest treasure in hand. It also isn't going to draw you more if that +1 card doesn't draw you another treasure. The point is that it could draw you more, potentially a lot more. And it's never going to draw you less.
Also, 20% is a pretty big deal in the long run.
The potential benefit is much higher than what you could do with Pearl Diver
Let's say you're about to draw 1 card with a cantrip and then play Storyteller; it'll be normal to want to play the cantrip first. Let's further assume that this next card won't be a treasure. If you first play a Pearl Diver to move a treasure from the bottom of your deck to the top to draw with the cantrip, and then play Storyteller, you've achieved the same level of in-situ deck shifting as the Storyteller-shifter variant would offer you in a situation where that treasure was already on top of your deck but you didn't have a way to get it into your Storyteller hand.
So I don't see how the potential difference is much higher than what a Pearl Diver does. The difference is where that treasure you wanted happens to be relative to the rest of your deck and hand, which is all more a matter of shuffle luck than anything.
It's nice when you get a +1 sift effect falling within the chain of whatever you're doing to improve your shuffle luck. There is potential benefit to be had! But it's situational to the shuffle you got, and in most cases won't make a difference.
The difference is that all the benefit you are describing for Pearl Diver is not coming from Pearl Diver itself, but rather two
other cards aside from Pearl Diver. You are repeating that mistake that Witherweaver
already pointed out.
Maybe you're using the word "sift" differently than how the rest of us use it. When I think of sifting, I am thinking about cards that let you cycle through junk. Some examples include Cartographer, Warehouse, Cellar, Catacombs, Oracle.
With this in mind, Storyteller certainly isn't a traditional sifter. The way I see it, its sifting comes from when it plays a treasure card. A Copper is converted into a new card. In a sense, you have just sifted that Copper for a (hopefully) better card. If you play something bigger, you get more cards. Hopefully the 5 cards you draw is better for you than that Platinum would have been
So let's consider a case where it makes no difference -- when the top card of the deck is, say, an Estate.
Storyteller gives you +$1. You play 0-3 treasures, then you draw. The +$1 from Storyteller translates directly into +1 Card, which draws that Estate.
The Storyteller variant gives you +1 Card immediately. We draw that Estate, just like the regular Storyteller. You play 0-3 treasures, then you draw. The effect is essentially the same. Where is the 1 card difference of sifting?
I don't think there is a difference in sifting unless you actually find a treasure that you want to play with Storyteller. Let's consider a case where it makes a small difference -- when you have no treasures in hand and the top card of the deck is a Copper.
Storyteller gives you +$1. You then draw a Copper. That is all.
The Storyteller variant draws you a Copper. You play that Copper, you draw again. You just sifted and cycled to 1 more card that you otherwise would not have drawn. The difference is even bigger when you find cards that are better than Copper.
You've been saying that the variant gives you a 1-card sifting difference and that it usually doesn't make a difference. Well, I'm saying here that either the two cards have 0 difference in sifting OR it actually does make a difference.
I've tried to be as clear as possible here about what I consider "sifting". Maybe if you give us
your definition and explain how it applies to Storyteller, it will help us understand what you mean.