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.
I am not racing ahead. I am simply traveling along in a lane until it ends and then merge at one, predictable/marked point.
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.
And yet that is not reality, so we have to deal with what we get. I will make the same argument in reverse- if everyone did NOT allow people to merge randomly before the merge point, both lanes would move smoothly at the same speed. But they don't. You sit in the "wrong" lane (the one that doesn't end), 1/4 mile before the merge point watching one person after another after another in front of you allowing more and more people to merge and your lane gets slower and slower and slower. Those "merging people" from the closing lane stop all the traffic in the other lane from flowing until they get what they want, and then suddenly they all can move again much faster, until the next person decides it is randomly the correct time to merge before the merge point.
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.
That seems like a reasonable explanation. Perception is often reality for lots of people.
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?
Actually, the capitalist mindset would be "I am buying more than others, so I should get special treatment", or "I have more money, so I demand a faster/better line for we people willing to pay more"
Sounds a lot like the extra 25% add-on fee on the admission ticket at Universal Studios for the the "express pass", allowing you to get/cut in the front of any ride line (yep, that actually exists.... it does at Disney too, but there is administered "fairly" because it is supplied to everyone at no extra cost and is limited).