First of all, it is quite probable that the LED traffic lights do flicker and here is why. Most of the LED lamps have been retrofitted to systems designed for incandescent bulbs. These bulbs used dimmers to reduce light output at night. The dimmers are of the phase cut variety where the actual power control uses a TRIAC. A TRIAC is switched on using a pulse and is held on by the current flowing through it. The current supplied is AC and so when the current falls to zero during the cycle the TRIAC switches off. Brightness is controled by the timing of the pulse relative to the AC waveform. LED lamps do not not play well with phase cut dimmers because, using less current than incandescent bulbs, there is often not suficient current to hold the TRIAC on, this is especially true at night. The result is flickering which may occur at any frequency and may not be related to the AC supply frequency. It is possible to get LED lamp units that have circuitry designed to play with phase cut dimmers, it is also possible to use load resistors in parallel with the lamps to increase the current.
The photo detectors (rods and cones) in the human eye are concentrated near the center of the eye with a very much reduced concentration towards the outside of the retina. The response time of the detectors and the time over which they integrate light levels is different in the center and in the outer edges of the retina. Also, the way in which connections are made to individual nerve fibres is different. The end result is that the center of the retina is designed to give good colour discrimination and high deffinition. The outer edges of the retina are designed to detect changes without a lot of colour detail or high definition, this is useful for detecting threats, who cares if it is an orange tiger or a yellow lion, you still need to run.
I think that what is happening is that the flickering is removed when viewed in an area of the retina with high concentrations of rods and cones but not when viewed in an area of the retina that is designed to provide early warnings. There is also some processing going on in the brain too.