PWM could be combined with a capacitor in order to smooth the voltage out. Or sufficiently high PWM frequency can be used (10s of khz), in order to avoid eye strain.

The former approach might negatively affect the efficiency, though, depending on where the efficiency peak is.

A constant current source does not have to be linear, one can use a switchmode powersupply with current regulation. Then the current though the LED flows in a continuous manner.

Switch-mode regulators don't pulse?

How wrong am I to think that a capacitor after the PWM-regulator would give a reasonably good approximation of a constant voltage?

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.