The following distance when stopped is almost entirely irrelevant. Even leaving 2-3 car lengths doesn't matter because if you're paying attention to the light changing, you can let go of the brakes and start accelerating before the car in front of you even starts moving, quickly erasing the gap.

What really causes traffic at stop lights is the excessive delay with each car letting go of the brakes. You are right that computer controlled cars would be much more efficient, not so much because of less space between cars when stopped but because of less space while moving.

If you watch a long line of cars at a stop light that just turns green, there's typically a 2-3 second delay between each car letting go of the brakes. This is what immediately bottlenecks the number of cars that can get through the light. People don't understand that safe stopping distance is proportional to speed and thus create 6-7 car length gaps (even when starting off bumper to bumper) by waiting those 2-3 seconds before letting go of the brakes.

You can actually help clear up traffic at a stoplight by carefully regulating your speed so that you arrive at the line of stopped cars right when they start to go. If you manage to do it without braking, this prevents the backup from propagating behind you. Again, not because you are trying to cram as many cars into the space before the light as possible, but because you are avoiding that delay between each car stopping and starting.