The circuitry isn't necessarily more complex. Often times it can be much simpler. Since for all practical purposes, an LED will have a near-constant voltage drop, you can use a resistor to set the bias current. All it takes, then, is an adjustable resistor, or potentiometer, which are commonly found in devices with knobs that adjust dimness. The knob just controls the resistance between two terminals, which adjusts the current. This method, though, isn't practical if you want to avoid physical adjustment of anything. You could do something using op-amps in feedback and a DAC (Digital-to-Analog converter) that allows digital control, but this requires a lot of parts, and in general manufacturers try to keep component costs down. This is why integrated solutions are so popular.

PWM isn't trivial either, though, often requiring a dedicated IC in certain applications (e.g. switched-mode power supplies). A simple on and off can just be achieved with a single digital output (and usually a transistor to act as a switch). But these digital outputs aren't well-suited to act as PWM controls, since it would require very low level. This is why microcontrollers often have a dedicated timer module that can generate PWM independently of the rest of the program running.