Earlier quoted context omitted.
If you require cars to use the bike lane, it's not a dedicated bike lane anymore. You bring cars and bikes together, and risk collisions between the two. It works only if car drivers are very aware of the presence of bikes, and trained to watch out for them. I think this is more likely to work in cities with an established bike culture than in car dominated cities. When cars dominate, give bikes their own bike path.
You bring them together regardless at every intersection unless you give the bikes their own crossing signal every block. The bike/turnlane makes turning into a two-step operation - first check for bikes, then second check if your turn is safe. That elevates the normal consideration bikes would get in a turn, which is none at all from most drivers.
It works in Copenhagen, since drivers just wait until the bikes have stopped streaming past — sometimes, only one car turns right through a change of the lights. I don't see that working in the US.
Give the bikes their own traffic light phase, at the same time as parallel pedestrians.