Sure they pulse/switch, but that is into/from the inductor/capacitor used as intermediate energy storage, not through the load (LED). At the output a constant voltage is seen (plus some ripple).

A capacitor on PWM output will give a decent approximation, _if_ it is big enough. For large LEDs this can be very costly (relative to other parts in system). Though the inductor in a switching converter is also a big cost driver.

Both for the capacitor, inductor and wrt to human perception increasing switching frequency helps. So that is what modern designs focus on normally.

A challenging aspect of LEDs is their nonlinear voltage versus current characteristic. A small change in voltage gives a very large change in current, and thus in output power. The characteristic is temperature dependent and has per device variation. Hence LED drivers are usually constant-current sources, ie they measure and attempt to regulate the current.