I'm not really in the industry. But I know that high-voltage MOSFETs / IGBTs need substantial amounts of current to turn on / off adequately. Under typical use, there's a dedicated chip called a "Gate Driver" that provides that current, between a microcontroller and the IGBT.

Its not that the IGBT / MOSFETs are built on these microcontrollers. Its that the Gate-Driver can be integrated into a microcontroller (simplifying the circuit design and reducing the number of parts you need to buy).

Under normal circumstances, a microcontroller can probably source/sink 1mA (too little to adequately turn on an IGBT). You amplify the 1mA with a gate-driver chip into 100mA, and then the amplified 100mA is used to turn on/off the IGBT.

By integrating a gate-driver into the microcontroller, you save a part.