I understand (more or less) that this flickering is the result of alternating current and the LED's binary nature, it's either on or off; and because it runs cool there's no "afterglow" of a hot filament to provide incandescence.
LEDs are not “binary” at all — the current can be freely adjusted (within the thermal power limits of the LED) to change the brightness. The problem with LEDs is entirely the second part: their light output is instantaneously proportional to the current, so unlike incandescent filaments, all of the “flicker” present in the input power appears as light.
Therefore, to avoid flicker, a LED driver (power supply) running on AC must include energy storage (usually in the form of capacitors or inductors) to maintain the same power input to the LEDs over the 1/60 or 1/50 second period of an AC cycle. If you see a LED bulb fade slowly when powered off, this is probably mostly due to those capacitors and not due to the phosphor. (Side note: Phosphor persistence would result in yellowish light, because white LED bulbs work by combining blue LEDs with a phosphor mix that converts some of the blue to other wavelengths that add up to yellow.)
Dimmer compatibility is another problem: conventional light dimmers work by cutting out an adjustable portion of the AC cycle (making it 0 volts instead of the usual waveform). This works poorly for “non-dimmable” LED bulbs because the output of their power supplies that drives the LEDs does not, like incandescent bulbs do, have a simple proportional(ish) relationship between the total input current and output current. Instead, there are various possible behaviors such as drawing a surge of power at the peaks of the AC waveform (simple rectifier-capacitor power supply) or shutting off entirely and “rebooting” every cycle (switch-mode power supply with insufficient storage capacitance).
Good dimming behavior comes not from simply throwing capacitors at the problem (which will make a bulb that can't be dimmed very much), but from power supply controllers that detect the incoming truncated waveform, derive the dimming % from that, and then produce a proportionally reduced output current to the LEDs. But that strategy then fails if the dimmer has an unusual output waveform the LED power supply isn't expecting.