Casting some spells requires particular objects, specified in parentheses in the component entry. A character can use a component pouch or a spellcasting focus (found in “Equipment”) in place of the components specified for a spell. But if a cost is indicated for a component, a character must have that specific component before he or she can cast the spell.
Does requiring "a copper piece" mean that a "cost is indicated" and so it requires one to actually be holding a coin, rather than just using a spellcasting focus or component pouch? Usually a cost being indicated is worded like "something worth at least 25 gp", so since this isn't phrased as "a copper piece worth 1 cp" or even "a one-cp coin" I'm not sure that it means that a "cost is indicated". It seems to more just be describing a random object associated with the spell like other "normal" spell material components. But then again, I can see a good argument that a coin used for currency would be the most straightforward way of indicating a cost that there is.
Obviously in general adventurers won't usually have a lot of trouble finding a copper piece during their travels, but I could imagine some circumstances where it would be inconvenient for a spellcaster to need to dig a coin out of their pouch while their spellcasting focus is already in hand.