How do we know that current doesn't get "stuck" in junctions?
The economist George Box once said that "all models are wrong; some are useful". If you asked a physicist they might be able to describe a particular set of circumstances...electric field, magnetic field, quantum effects, whatever...that would cause a temporary nonuniformity in the carrier concentration in a wire.

But we are engineers here. Our models need to be useful. We don't need to prove that a model is correct...because we know that it is not correct. Nevertheless, we know that the model is useful and it works for our purposes.