You're one of the ones I get crazy and annoyed at who races ahead to break into the single line that's trying to get through construction. If everyone were to get into single file while speed is still high, way ahead of the bottle neck, then there wouldn't be any choke down/slow down at the bottle neck.
I used that as an illustration of the human nature; not to make a direct comparison to shopping lines. People would rather THINK/PERCEIVE they are getting into a shorter/faster line, even if it is not faster, than get into your long line, even if it is faster. A long line appears to be bad and people don't want choice taken away from them.
When you say, "I don't want to pick," (I want someone to pick for me) "I don't want to decide," (I want someone to decide for me) and "I know it will be fair to everyone," (I want an equal redistribution of waiting in line), then you express an explicit socialist mindset. The American democratic/capitalist mindset says, "I want to pick," "I want to decide," "First come, first served." What does fair have to do with anything?