> To clarify, claiming current is the derivative of charge is like claiming the current of a river is the derivative of it's water level.

My electro mag skills are a little rusty, but I don’t think that’s the right analogy. You wouldn’t say that the speed of a runner is the derivative of their height, similarly when someone is running you wouldn’t try to say that their speed isn’t a derivative of their height, as their height is more or less constant “for the length of the run”.

Similarly, it isn’t the height of the runner, but the distance they’ve covered, it isn’t the depth of the river, but how much water has passed through, it isn’t the static charge of the wire, but how much charge has passed through.