If you are controlling the pulse width then not using a DC restore circuit will mean that at a high value of duty cycle, the peak voltage from the transformer will not be enough to properly turn on the MOSFET. This is because the output of a transformer must have an average value of 0 volts and if the original pulse shape is 10 volts for 90% of the time, it will become 1 volts for 90% of the time after the transformer.

If you are controlling the pulse width but not using a DC restore circuit, it will mean that at a high value of duty cycle, the peak voltage from the transformer will not be enough to properly turn on the MOSFET.

Fact: the output of a transformer must have an average value of 0 volts and if the original pulse shape is 10 volts for 90% of the time, it will become 1 volt for 90% of the time after passing through the transformer: -

This is a simple simulation that shows what I mean. The input to the transformer goes between 0 volts and +10 volts (blue trace). It is capacitively coupled (1 uF) to the transformer primary. The red trace is the output of the transformer into a 1 kohm load.