It's not even like artifacts. Artifacts can be used in every deck, every faction... You can usually go with one artifact removal, considering a good number of them have side effects and by now people know what kind of artifacts are worth removing. And apart from Eldain decks, decks rarely run more than one of two artifacts. Same with lock/unlock, status/purify, big unit/big unit removal... It's all mechanics that you can find +/- at least once in every deck.
A card to remove coins would be a terrible idea as it would be a tech card that is ONLY useful against SY. The only way it would be viable is to actually add that function to already existing cards on top of their other abilities. Otherwise what? You will run one "remove coins" card to tech against SY? 1st, it's not gonna be enough, and SY decks already have more than enough profit cards to replenish their stock. 2nd It would be perfectly useless against other factions. It reminds me of the Roche:Merciless from beta that destroyed an ambushed or as 3RMED said a couple times Lambert:Swordmaster. Running a purify, an unlock or a polyvalent artifact removal is rarely a loss, but who wants to spend provisions on removing coin cards?
The best way as I see it for now (and I obviously am no expert and probably missed other options) would be to link the coins to units somehow. Either when earned, you can "attached them" to units instead of storing them in an untouchable bank, or leave it as a general resource but penalize the loss of cards, or the loss of profit cards.
I mentioned before loosing units could trigger a loss of coins in general, but what if for example every time a unit with "profit" is destroyed, you loose that many coins? That would make the double "profit"/"fee" cards more risky to keep, that would make stocking up coins riskier, that would make hoard harder to attain...