You may use a step-up transformer to increase the voltage between the wires which carry the voltage to the city (where the voltage is converted again down for the electricity consumers). But you are not going to increase the voltage between the ends of one wire, you prefer that the voltage drop in a wire reduces. Consequence: No growth of longitudal electric field in a wire. That electric field and the mobility of electrons are related to current in a wire.
The transversal electric field between the wires is related to the transfer voltage and it shouldn't used to calculate the current in a wire by applying it only to the electrons in the wire.