This doesn't sound very square to me.
I'm totally amazed at how some cities do not have protected left turn signals. During high traffic times, this means you can litterally never have a gap. Which leads to the situation where once the light turns red, 3-4 cars wanting to turn left run the red light. LA was the worst of the places I've experienced this.
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.
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.
These people have little reason to got Lowell/Leominster/Worcester/Fall River (one ring outward) or Providence/Hartford/New Haven/Springfield (one ring further still) so Boston is just what they complain about.
If Lexington or Sudbury is your frame of reference then Boston is a f-ing zoo. If Lawrence is your frame of your reference Davis Square (or Kelly Square) is same shit different day.