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.

Have to admit I never paid much attention to what it was, or when, other than thinking it was kind of cool. I figured it was so the blinker was more visible, but it was more an idle thought than anything else. Kind of thought about the issue of half your forward visibility going away when changing lanes when I was typing my response.

Have to say, though, that if the DRL turns off so you can see the turn signal, and the headlight doesn't, then there ain't no way someone is seeing the turn signal with the headlight on. The headlight is brighter than the DRL, so it would have to mask the turn signal like you are saying it isn't supposed to.

Have to add that I sometimes wonder why anyone puts turn signals on cars anymore. Seems kind of rare to see them used. :-)