Unless you want it to counter handsize attacks, can't it say, "When you gain this, +2 Cards at the end of this turn"?
It’s to make it easier to not forget. I play most of my dominion in person, and it’s quite easy to forget stuff like this. The two cards being set aside is the visual reminder. Without the set aside card it could be easy to forget, especially if you gain it in the start or middle of a big turn. For example, the river’s gift stays until clean up to be a visual reminder. But this card is gained and can’t be a reminder, so the set aside cards ARE the reminder. Expedition doesn’t do this because your buy phase is almost always near the very end of your turn.
There’s enough mid-turn 4 cost gainers that I thought it was relevant. I’m open to being persuaded to the simpler wording, but the “reminder” is the main intention.
It does have the benefit of soft-countering militia attacks (self-junk instead — design neutral for me). It also has the downside (that I consider a design positive ) that it fails in deck-drawing scenarios: it either prevents you from drawing 2 set aside cards this turn, or next turn it might only draw the estuary if you’ve already drawn your deck.
Anyway, when first designing I thought of all of this, and thought the wordier phrasing was a better overall design.