A microcontroller can be bought as a chip and used as such. But it can also be part of a digital design, a system on chip with embedded software (firmware). Hence if the application requires a microcontroller, you could use a controller chip and some discrete components. If the controller needs hardware accelleration, additional (communication) interfaces, … then an application specific design can be considered. Then you can implement what you want. Protoyping and low volume products can use an off-the-shelf solution, an FPGA. It can be reconfigured many times. If the volume is high enough, an ASIC can be considered. An ASIC is expensive to develop therefor it is only interesting financially to spread this cost over a few million products sold.