Sure, if the line perfectly rebalances then three lines is almost identical to the single line.
BUT as I'm sure you know, it's sometimes hard to know when to move. Is it after you've waited one minute, then hop to the back of another line?
Let me give you a concrete example: Imagine you enter a line with 15 people in it. Your line moves 14 people through perfectly. You're next, but the guy in front of you takes longer -- maybe he can't make up his mind about wanting some bubble gum. Do you hop to the back of another line and wait 15 more minutes (because the average queue length is 15m) or do you wait it out while this guy in front of you goes? How long will this guy take? 1 more minute or 30 minutes?
And of course, once you hop to the back of another line, the guy from your previous line finishes, and there's someone else in your new line who takes forever. Then you're even more upset that you switched lines!! :-)
With a single line you remove the need for an oracle, which you need for the n-line scenario.
To add to your examples, there's also the case that you've already unloaded your cart, but the idiot in front of you sends the cashier on a wild goose chase to get cigarettes for him and they spend ten minutes sorting that out. Or you're behind some "extreme couponer" who splits their order into six separate orders to maximize their coupon savings, and you have to resist the urge to just pay for their entire order just to shame them into being less of a goddamn miser.
And then you CAN'T leave the slow line because there are people boxing you in from behind, even though you chose this line because the guy ahead of you had only one item... until he decided to make the cashier search the entire store to make sure they were actually out of his favorite cigarettes.
BUT as I'm sure you know, it's sometimes hard to know when to move. Is it after you've waited one minute, then hop to the back of another line?
Let me give you a concrete example: Imagine you enter a line with 15 people in it. Your line moves 14 people through perfectly. You're next, but the guy in front of you takes longer -- maybe he can't make up his mind about wanting some bubble gum. Do you hop to the back of another line and wait 15 more minutes (because the average queue length is 15m) or do you wait it out while this guy in front of you goes? How long will this guy take? 1 more minute or 30 minutes?
And of course, once you hop to the back of another line, the guy from your previous line finishes, and there's someone else in your new line who takes forever. Then you're even more upset that you switched lines!! :-)
With a single line you remove the need for an oracle, which you need for the n-line scenario.