Another way to say it is that, with a superconducting wire, you can make the wire as thin as you want and still pass the same amount of current through it, without melting the wire. Picture using a USB-C cable to charge your car.
† (There'd still be a current limit due to the heat generated by the chemical reaction that rebuilds the battery's voltage potential... if said reaction is exothermic. Some battery chemistries are endothermic when charging!)