I think that most of us are missing the point.
(pre-PS: I'm going to assume a utopian society where people actually USE their turn signals
)
Where turn signals
really earn their keep is when a vehicle is about to change lanes (which, in effect, includes turning off the roadway; but I'll stick with lane changes for the moment). Giving the signal before changing lanes notifies drivers nearby, including the one sitting in the blind spot. They can either make sure that there's room or honk to warn the first driver that they can't move.
One big difference between bicycles and cars/trucks/motorcycles/buses/scooters is the speed differential. You're just not going to have a motor vehicle nearby for more than a few seconds (unless you're in a traffic jam, in which case you'll probably be moving faster than everyone else anyway). There's little use, then, in lighting up a turn signal.
Making a right turn on a bike (on right-hand drive streets, that is) doesn't affect surrounding traffic very much; giving a hand signal is as much of a courtesy as anything else, probably appreciated more by cross traffic waiting at the intersection than by the people behind you.
Making a left turn across the street
shouldn't affect traffic very much, either. If you're crossing over safely, you're using a large enough gap in traffic that you won't be forcing people to jam their brakes (and, most likely, causing a rear-end collision somewhere behind them... which is in another thread). So, then, there's nobody near & to the rear that needs to see a signal.
I figure the safest way to ride on the street is to ride as if nobody can see you -- don't
depend on their attentiveness for your safety. I still think that good headlights & taillights are necessary, and a brake light is a good idea (and easy to implement with a B&M DIWA generator setup). But, I think that turn signals just aren't necessary.
IMO.