[nandemo]

It's not at all obvious to me that one line is always faster (but then I only have a master's degree :-)). It might be faster in some situations, maybe slower in others.

In particular, the one-line system might significantly increase the average distance between (first-in-line) customer and nearest free cashier. Also, when there's a lot of cashiers, the customer might take more time to notice where is the nearest free cashier. I saw that happening the last time I checked-in for a flight.

In contrast, at immigration there is a long, single line but also short lines (1 to 2 persons) in front of each "cashier". These work as "caches" that minimize the delay I mentioned above.

[URSpider94]

As others have mentioned, one line feeding small cache lines is probably closer to reality, for the reasons that you mention -- buffering so that the cashier is always occupied.

The main goal is to prevent a single "price check" from jamming an entire line of people -- keep the queues at each station as small as possible so that most customers can route around the blockage.