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.