Here's another way to make the point:
Claim 1: "Coppersmith is the only card that changes the effect of playing another card."
Claim 2: "Copper changes the effect of playing Bank."
One of these claims must be wrong (or at least incomplete). You tell me which one.
I think Claim 2 is wrong. The issue here isn't a question of the semantics of what it means to "affect" another card, the issue is that there are 2 possible definitions of the word "effect." The OP meant the specific Dominion-related definition of "the steps you take when you play a card." There is also a more general definition of "effect," which is more like "the net result of playing a card." In the second definition, yes, copper changes the effect of playing Bank.
However, looking at "effect" as "steps you preform when you play a card," then when you play a Bank, you preform the same steps, no matter what treasure has been played: count how many treasures are in play, and get that many coins.
But the effect of playing Copper has actually changed. If you've played a Coppersmith, you cannot preform the steps listed on the Copper card, which is "get 1 coin." That step is gone, you now preform a new step instead, which is "get 2 coins."
*Edit* rinkworks seems to have said the same basic thing...