I'm thinking more along the lines of why I would run a red on a bike and not in a car. The reason is that a car is different. A car has much less visibility. Once in motion, if a car should come out of nowhere, it cant stop and turn around quickly like a pedestrian or a bike. Getting around on a bike is already considerably slower than by car. In many areas, on a bike, you end up getting caught by many more lights because you are unable to take advantage of the synchronized timing of multiple lights that were programmed for cars. If I stopped at every light downtown at 6AM when the streets are pretty much clear, It would add a LOT of time to my route and not my trip any safer.
Maybe the op feels stupid because he knows its completely safe to cross but sits there anyway. There are several intersections around town where the lights switch to flashing yellow late at night until rush hour in the morning. A lot of this discussion could be avoided if they did that more. There are many cases where it is silly even for a car to sit there for 3 or 4 minutes without a car in sight. The controls are really there for the busy times, but its too much work to program them differently for different traffic load times.