Pearl Diver is a sad sad Dominion card that is sometimes not even better than nothing. It is one of the worst $2 cost Dominion cards in the entire game. I will explain why.
Using Pearl Diver
Pearl Diver simply draws a card and looks at the bottom card of your deck. If it is a good card, you will top deck it. Otherwise, you will leave it on the bottom most of the time. To put simply, Pearl Diver slightly mitigates bad shuffle luck, and only sometimes. That’s it.
Why is Pearl Diver so bad then, if it at least is a cantrip? Pearl Diver’s use often does not outweigh the cost it takes to get one. Getting nothing can be better than Pearl Diver.
Suppose an opponent plays a discard attack on you, and you have Pearl Diver and some other cards in hand. You can take a gamble and hope to draw a card with Pearl Diver, or discard it. If you did not have Pearl Diver, you would have known what card you would have drawn anyways with the Diver, making a more effective choice as to what to discard instead. In those cases, having a Pearl Diver is worse than nothing.
Ignoring Chapel, $2 cost cards in Dominion generally have some sort of use, even when they are poor. Haven sets aside a card for next turn. Pawn provides flexibility with +buy. Raze trashes and cycles at the same time. Even lowly Herbalist provides a much needed +buy sometimes, and maybe you topdeck a Fortune. Heck, you might put a copper on top to help block Masquerade!
Pearl Diver has none of these edgecase uses with its ability. There is nothing in the entire game that makes Pearl Diver's ability all that desirable.
On the bright side
Not to say Pearl diver does not have its uses. Cheap cantrips are a boon for Teacher engines, and Pearl Diver is certainly not the worst card in the $2 category for this. Pearl Diver is also an action card, which can boost Vineyards and help piledrive Peddlers, as well as activate Heralds and Scrying Pools. However, this is more of an effect of Pearl Diver being a cheap cantrip or just being an Action card more than it is for Pearl Diver’s ability.
To put this entire article into a sentence: Only pick up a Pearl Diver when it helps another strategy along.