Yes, and that's dangerous and what's wrong with mixing zones - forcing cyclists to merge with fast-moving cars endangers them. It's much safer to treat bikes like fast-moving pedestrian traffic crossing with the light; let them keep moving and turn perpendicularly across the bike lane.

Yes, that means the car should come to a stop if there are cyclists oncoming, but you'd do the same in courtesy to pedestrians in the crosswalk or to cars coming he other way while you make a left turn.

When a car is turning right and a bike is continuing straight, the bike is moving much faster than the car, through a narrow and obstructed window, from behind. The chances of the driver seeing you coming are low.

When designed well, the parking lane stops and becomes a turn lane. The car is responsible for merging across the bike lane in one action, and then making the right turn in another. This happens while there is less of a speed differential, and because it pulls over, it's obvious to the bike that it intends to turn right.

The amount of sidewalk you have to scan to see if there will be pedestrians in the crosswalk in the next ~5 seconds is tiny, whereas the amount of bike lane to scan is essentially the whole block.