Given that the most important role of a light is to be seen by others on the road and how short your batteries last for especially bright lights, blinking is a fairly natural feature to add to lights. By making the light blink, you make the light much more conspicuous and allow a very powerful light to be seen from a much longer distance than a less powerful light that is on constantly.
There are, of course, laws to be considered. Some states and countries forbid blinking lights. Furthermore, many brevets restrict the use of blinking lights only to cyclists in distress.
Now, back in the earlier days of LED bike lighting, designers stuck to a simple on-off pattern that could be implemented with a minimum amount of circuitry. But these days, a lot of bike lights are made with a single semi-custom chip either epoxy-blobbed directly to the board or in a custom package because they also want to make the light such that it doesn’t dim as the batteries get low and requires fewer batteries. PlanetBike with their SuperFlash being a primary example.
I have some thoughts on the subject, and I’ve checked some research studies on the subject:
Consider Photosensitive epilepsy. If you want to never trigger it, you cannot blink faster than about 2 Hz, At 5 Hz, you will trigger seizures in about 5% of the population. At 10 Hz, 65%. I checked my PlanetBike SuperFlash and the two little lights blink at around 10 Hz. Granted, people with photosensitive epilepsy are not allowed to drive if they are still prone to seizures, but they might be found walking or bike riding. So this is something to consider.
On the other hand, research does show that the faster the blink rate, the more urgent it seems. However, I suspect that, like center-mounted-brake-lights, this effect goes away if everybody had a fast-blinking blinky.
Most of the research on effectiveness of blinky lights is confined to motor vehicles, which always have headlights, tail lights, and running lights, so it’s hard for me to make a bulletproof argument about lights that change in intensity as compared to lights that blink fully on and off. I suspect that at least some degree of constant lighting is necessary and just blinking is not enough, which is why I usually run several lights on my bike.