Many cheap LEDs flicker at at double line frequency (100Hz or 120Hz depending on the country), because they're driven by rectified AC power with inadequate filtering. Pulsing LEDs only increases efficiency at low brightness, e.g. 7-segment displays, not room lighting. See:
http://donklipstein.com/ledp.html
The flicker fusion threshold for many people is above 60Hz. Remember 60Hz CRTs? 85Hz is a more reliable threshold. And in any case, flicker fusion threshold is only relevant when your eyes are stationary. On eye movement you get phantom array effect. People vary greatly in how sensitive they are to this, and depending on how strong your saccadic masking is, it can be annoying at frequencies well into the kilohertz.
How does pulsing at a frequency that's unrelated to the AC line frequency but still low enough to be visible improve efficiency? SMPS efficiency usually peaks in the hundreds of kHz, which is invisible even to the most sensitive observers.
You said "LED flicker usually has nothing to do with AC power." But most LED lighting flicker is the result of using a capacitive dropper power supply. These are cheap and efficient, but produce a lot of ripple at double the line frequency (with full-wave rectification). Filtering the output enough to make flicker imperceptible would cost more, and not everybody notices the flicker so it's easy to get away with cutting corners. See:
The flicker fusion threshold for many people is above 60Hz. Remember 60Hz CRTs? 85Hz is a more reliable threshold. And in any case, flicker fusion threshold is only relevant when your eyes are stationary. On eye movement you get phantom array effect. People vary greatly in how sensitive they are to this, and depending on how strong your saccadic masking is, it can be annoying at frequencies well into the kilohertz.