Indeed, older bulbs work in both directions and the voltage fluctuation isn't visible in the light emitted, because the thermal mass of the filament smooths out the alternating current into a continuous glow.

But LEDs will flicker unless the AC is rectified and smoothed out. Cheap lights will just not come with the circuitry to do this, as you can just hook up the diode directly, the only drawback being it will only emit light some of time. 60Hz is slow enough that you will notice it, however. Especially with movement, it makes reality look like it's running at 60fps.

Even when rectified, unless a capacitor is added to the circuit, LEDs will flicker. AC merely rectified will still have the voltage hitting zero 60 times a second, otherwise.