The magnetic flux of the transformer core is related to the applied voltage. The excitation current does not increase with the addition of the load in the current. Although adding a load to the iron core will not make it full, the automatic screw locking machine will increase the resistance loss of the transformer coil. When crossing the rated capacity, the heat generated by the coil cannot be dissipated in time, and the transformer coil will be damaged. Assuming that the coil you are using is composed of superconducting materials, increasing the current will not cause heating, but there is still impedance caused by leakage magnetic flux inside the transformer. However, as the current increases, the output voltage will decrease. The larger the current, the lower the output voltage. Therefore, the output power of the transformer cannot be infinite. Assuming you say again that transformers have no impedance, a particularly large electric force will occur when current flows through the transformer, which can easily damage the transformer coils. Although you have an infinite power transformer, it cannot be used. It can only be said that with the opening of superconducting and iron core materials, the output power of transformers of the same volume or weight will increase, but not infinitely!

The simplified schematic diagram of a transformer shows that when a sine communication voltage is applied to both ends of the primary coil, there is alternating current and alternating magnetic flux in the wire, which passes through the primary and secondary coils along the iron core to form a closed magnetic circuit. In order to maintain the existence of magnetic flux, a certain amount of electrical energy consumption is required, and the transformer itself also has certain losses. Although the secondary is not connected to the load at this time, there is still a certain current in the primary coil, which we call no-load current. It can be seen that there is a close relationship between primary current and secondary load. It can be considered that the power consumed by the secondary load of a transformer of interest is the electrical power obtained by the primary from the power source. Transformers can change the secondary voltage by adjusting the number of turns of the secondary coil as needed, but cannot change the allowable power consumption of the load.