It has nothing to do with the voltage. If you had 120v AC at 0.5Hz, you would be able to see a light bulb slowly brighten up from zero, dim down again until it shuts off and repeat the whole thing once a second. If it was two LEDs hooked up back to back, you would see one light up, then fade away, then the other polarity light up, fade away and alternate. By definition, alternating current is discontinuous power delivery. There is absolutely no getting around this "power outage" without using capacitor on a single phase power. You absolutely have to have a capacitor in order to keep the light from dropping to zero, or ideally not even close to getting to zero. Lower the frequency, larger that capacitor has to be. The capacitor inside a high quality fluorescent ballast does this already on the 60Hz side and you don't really need to fill the gap on the 40,000 Hz as it is not visually perceivable.I'm under the impression that fluorescent ballasts put out several hundred volts AC.
Why would a high voltage be easier to convert than 120v?
There are capacitorless LED ballasts. Those actually fully blackout at each half cycle, 120 times a second. Traditional fluorescent lights do as well, but unlike LEDs, phosphors on fluorescent lamps have a considerably more afterglow than LEDs and it is enough to significantly reduce flicker.
If you were turning a DC generator with a single phase AC motor, the mechanical inertia of spinning motor and generator are doing the work of the DC link capacitor.