They think they're being polite, but they're forcing dozens of cars to wait for an additional cycle of the stoplight, whereas if they had just pulled through the light as normal then the waiting car would get a chance to merge as traffic either cleared or came to a stop again.
Obviously, optimal behavior is dependent of the traffic conditions.
Cars looking to merge should do so as the traffic comes to a stop. A car already on the highway they are looking to merge onto need only stop sooner than they otherwise would, allowing them to pull out into traffic that is already at a standstill.
Lets take "dozens" to mean "atleast 18" (a dozen and a half). The average car is 15ft so this means to fit the 18 cars bumper to bumper there will need to be at least 270ft between the car you let in and the car in front of it when it passes out of the intersection.
If you leave half a car length between cars and allow the full 2 dozen this number quickly becomes 528ft.
If people are really this slow in pulling out, I feel your pain. However it is these numbers that caused me to judge your anecdote as hyperbole
Additionally, you suggested blanket solution sounds more dangerous as well as completely unworkable in bumper to bumper trafic: "Cars looking to merge should do so as the traffic comes to a stop."
It's far more dangerous to pull out in-front of a moving and already braking car that may or may not see you then to pull out in-front of a stopped car that has indicated that it does.
The particular case is that a driver going straight will yield to a driver approaching from the other direction who wants to turn left across them. They should not yield. They have a green light.
I'm curious... where have you seen these troubles? Perhaps the small radius is the real issue?
The ignorance argument is difficult to agree with because every country has had to introduce them to an uneducated population at some point. You could have used the same argument against traffic lights.
The point of roads is not to transport any particular traveler at the greatest possible speed, but rather to transport all of us in safe and convenient fashion.
I think the second problem is an acceptable tradeoff, but ymmv
The first problem is the people who don't know how to drive. I cannot count the number of times I have seen people stop in the middle of a roundabout to let cars in, or stop at the entrance and stare in confusion when there is absolutely nothing coming.
The second problems is inherent in the design. A line of traffic that is going straight can, effectively, prevent any cross traffic from entering the roundabout, due to the small radius of most US traffic circles. This is a trade-off, of course, and is still safer than traffic lights or a 4-way stop, and usually more efficient.