Modern Headlights

Not quite -- this what you're seeing is not the headlamp (as such) turning off, it's the daytime running light (which may be the headlamp operated at a lower-than-normal voltage) turning off on the side the turn signal is operating on. That's required with certain kinds of DRLs and certain separation distances between the DRL and the turn signal. It's for daytime only -- it would be an extremely bad idea (not to mention illegal) to turn off the headlamps one at a time while signalling for a turn at night.

If you see this happening at night, it's because some dillweed is driving around after dark with daytime running lights instead of full nighttime lights on.