These people say otherwise about left-turns [1]. What you're suggesting only works if you're able to first cross the intersection safely on the right (debatable due to cars turning) before the light switches. A car would queue in the left-turning lane, which is usually deep enough so you can squeeze over if the light is already red up ahead and catch the signal. Left typically goes green just before the straight goes green again, so in most circumstances, a cyclist on the right hand side would have to wait for two light intervals. You also have to navigate twice the amount of lanes of traffic. Turning left in a car, you only have to navigate 1/2 of the perpendicular traffic on a stretch of road. If there's no light, this might be very difficult and dangerous to do on a bicycle.

1: https://bikeleague.org/content/bike-lanes