Ok, I see now. I do see "$X (big coin)" and "this is worth $X" as the same as "+$X". They all mean "produce $X".
But about the basic idea of a coin property similar to the cost... It would mean that all cards have that property, not just Treasures, because all cards can produce coins. But cards can also produce other things, like actions and buys. To me there's nothing special about producing coins.
You could see Bank as modifying its own property, but then so would Mining Village (if you trash it), and even Pawn etc. And then you would need an action property and a buy property, which would be modified by all cards that can produce variable amounts of those.
To me it's cleaner to regard them all as instructions based on a number that is described in the instruction, just like "+2 cards" or even "gain 2 Coppers".
I wasn't proposing that
everything that gives coins (or even a variable number of coins) should key off of a "produces" property. Mining Village's ability should just be, like you said, an instruction based on a number that is described in the instruction. So should Salvager's. So should anything that says any form of "+$N."
The only things that I was suggesting should key off of a modifiable property were the things that an ongoing effect modifies. Specifically, for this discussion, the "abilities" represented by the big coin on Copper, Silver, and Gold (whose behavior is modified by ongoing effects from Coppersmith and Envious). And, well, the big coin should mean the same thing wherever it appears, so it can be treated the same way even on treasures that nothing cares to modify.
Even using that paradigm, it's up for interpretation whether or not a Bank operates by modifying its own copy of such a property. But I completely disagree that treating Bank as doing that somehow necessitates treating Mining Village as doing the same (and especially disagree that it implies anything at all about how actions and buys should be handled). The purpose of having the "produces" property wouldn't be to address the concept of a
variable amount (e.g. +$1 per something), as you seem to be inferring; the purpose would be to address the concept of an
ongoing effect (e.g. this card will now make $N whenever it actually produces coins). Just because a card like Bank
could use an ongoing effect to make itself worth a variable number of coins doesn't mean that
anything trying to give a variable number of coins
must or even
should do so via that mechanism.
If you wanted to argue that an ongoing effect is not necessary for expressing what Bank does, and that it is simpler to have it just determine N and then do +$N, I could see your point. The reason I was treating it as an ongoing effect is just that there exist ongoing effects that modify the coin values of some treasures, so I imagine all treasures as being potentially modifiable in the same way. That and the wording "this is worth $N" suggests an ongoing effect to me.