Purpose of gate driver in Class D amplifier
Power MOSFETs typically have a fairly large gate capacitance, thousands of pF. The output current drive of a "standard" comparator will be in the mA. Combine the two and you get a level transition of the gate voltage changing slowly, where slowly means less than tens of nanoseconds. Slow gate drive means slow switching of the MOSFET load, and that causes the MOSFET to heat up, which negates the value of the class D approach. A MOSFET driver, on the other hand, can typically source and sink pulse currents on the order of an amp. This provides the speed needed for class D to work properly.