There are plenty of protected lanes in my city, but they just hide bicycles behind parked cars, making it less safe at every intersection.

The only way I can think that might work better would be to convert a 3-lane road (with suicide/turn lane in center), into a 2-lane road. The center lane gets converted into a two-way bicycle road - raised up like a sidewalk with curved curb. No left turns allowed for cars, only right turns. This way bicycles are visible and protected.