Visibility can be partially obstructed for drivers at an intersection due to surrounding cars. This can create a situation where a car that is stopped 5 cars behind me, or is coming from the opposite direction, might not be able to see me. The risk is compounded at intersections with multiple lanes, where visibility is further decreased, and I may need to wait in the middle lane due to the presence of a dedicated turning lane.
The act of just starting a bicycle from a full stop also increases risk. I wear pedals that require me to unclip when stopping, and clip my feet in again when starting. This can take a couple seconds (I don’t always get it on the first attempt), during which time my maneuverability is severely limited, and I may need to look down at my feet for a moment instead of watching other cars in the intersection. Even for people using flat pedals, it can require more effort to turn the pedals when stopped vs. moving slowly, which decreases maneuverability and increases time spent in the intersection. Riders are also more likely to wobble when starting from a full stop.
So it’s not really about saving time, although that is certainly a nice benefit, but rather about improving safety for cyclists.