One problem with using sheep or potatoes as your currency is that it is a bit unintuitive for the player. They might be unsure that this resource is really used only as a currency and doesn't fulfill any other mechanical purposes.
When you give the player a sheep, they will wonder what to do with it. Their first ideas will likely be to try to slaughter it for meat or shear it for wool. Or perhaps milk it of sheep's milk? Maybe it's a pet they have to care for? Perhaps they can ride on it? Perhaps it can be combat-trained and used as a companion in battle?
Trading it for other resources would be pretty low on their list of potential uses.
And then there is of course the plausibility problem. A resource which anyone can produce, which is perishable and which isn't perfectly fungible would not make for a very good currency in the real world. But that is of course an issue which can be handwaved away when this resource doesn't have any of these properties in your game.
But players will get over that eventually after spending some time with the game. Especially when you make sure your UI design and the tutorial make it clear that sheep are really just a currency and nothing else. So it's really not that much of a problem.