A class A no feedback power amplifier with just an input transformer, a MOSFET, an output transformer, a battery and nothing else?

At your risk. Please take all safety precautions. What if an enhancement MOSFET is used, it is on at 0 volts bias so that step up input transformer is directly connected between source and gate. Then output transformer (with air gap to avoid saturation by DC current) is conneted to drain through a battery whose negative terminal is connected to source to close the circuit. Thats's all folks.