> During high traffic times, this means you can literally never have a gap.

It is legal to enter an intersection (i.e. cross the white line) when your light is not red. Therefore at least one car can turn left legally per light cycle. Agree completely that this isn't good enough.

Pretty much all of the Cambridge and Somerville "squares" are really larger areas with nightmares of streets coming in and branching off at all sorts of random angles.

Left turn arrows tend to be eventually installed at the worst of the unprotected lefts. (Or left turns are just prohibited.) Locals just learn to expect a couple cars to do a left on red--and for another 2 or 3 to turn as soon as the light turns green.

The "square" presumably refers to the place (like a town square) and not the streets themselves.

Yes, just like Madison Square Gardens which is a round/oval shape building. People don't realize how silly words can be when one's inner child takes hold.