It’s very common to talk about currents in contexts in which the charge carriers are not electrons. For example, in chemistry, you often talk about a current of ions moving through a solution. From the perspective of (classical) electromagnetism, any two point particles with the same charge/mass ratio have exactly the same behaviour, so it’s common to talk about arbitrary charges, in the same way that a mechanics textbook will talk about general terms like “masses”, “objects”, or “bodies” instead of specifying that everything is, say, a brick.
If you mean that we should measure currents in electron-charges per second instead of amps, that would just be unwieldy for most purposes.
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