I think the problem here is that we're not all defining "effect" in the same way. tlloyd is defining "effect" by the ultimate outcome, as in: "Bank's effect is +$2 under these conditions, and +$3 under those conditions, so Bank's effect is different under the two conditions." Indeed, this is absolutely correct.
AJD, et al, is saying, "Bank's effect is +$ equal to the number of Treasure cards in play." Thus, its effect is the same whether 2 Treasure cards are in play vs. 3 Treasure cards in play. Mention was made in this thread of "atoms." Bank only has the one atom, and playing Treasures beforehand doesn't change what that atom is, nor does it change the atoms of any other card, played or yet to play.
Neither are unreasonable arguments. The former is player-centric: the player doesn't care what internal mechanism is at work, only how much money he can spend when all is said and done. The latter is game-design-centric: what matters is NOT the ultimate outcome but rather the specific function of each component of the machinery.
Both of these views are important, depending on the context of the conversation. In this one, though, a conversation about how individual cards actually work, I have to side with AJD. No, Copper does not change Bank's effect when played. Yes, Coppersmith does change Copper's effect when played.
Now, if Coppersmith were reworded thus: "After you are finished playing Treasures, +$1 per Copper in play," then I would agree that Coppersmith does NOT change Copper's effect -- even though the ultimate outcome would be the same. Because in that case, Coppersmith would be the card performing the effect. But it doesn't read that way: it says that, specifically, Copper does a new thing. And so it does.