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That's not strictly true. The very simplest of DC LED drivers flicker, such as the classic single-transistor battery saver circuit, but a slightly more complex DC LED driver circuit will not. One of the best ways to drive an LED is with a constant current source, which typically involves putting an inductor in series with the LED and switching the supply to that at a reasonably high frequency, which would mean the LED does not flicker at all.

If it's hooked directly to AC power, isn't there by definition a flicker? With a power IC, a poorly implemented power circuit will also visibly flicker. With high enough rate and the right power characteristics it should not be noticeable. Do you notice flicker in a quality phone or monitor screen?

Yes! And this after image is distracting.