The article should have clarified one more assumption: In a Landsburg's queue, it is compulsory for everyone arriving at the scene to *join the queue immediately*. Otherwise, people would just swarm around the head of the queue, fighting to join the queue as soon as the current customer gets served. In the following discussions, I assume such swarms are successfully prohibited.
# For those who end up going home
For those who end up going home, a traditional queue is still more efficient.
In a Landsburg's queue, if you decided to go home, it must be that there has been too many people joined the queue ("the queue got full"). *Their arrival takes time*. You would have waited for quite some time when you decided to bail out.
A traditional queue, on the other hand, allows those who end up going home to choose to do so immediately upon arriving at the scene. You arrive at the scene, look at the queue, judge that it would take unacceptably long period of time before you can get served ("it's currently full"), and decide to go home. You never join the queue. You wait for zero seconds.
# Arranging early arrivals is important
*Filtering for fans.* In the book _The Armchair Economist: Economics and Everyday Life_, Landsburg himself stated that some businesses would prefer to serve fanatic patrons over mediocre customers. In an ordinary queue, customers can prove their loyalty by *arranging to arrive early*. On the other hand, by attaching the probability of getting served directly to the probabilistic nature of when one arrives, a Landsburg's queue does not allow/support proving patronage with early arrivals.
*An ordinary queue is an auction.* One of the main arguments that Landsburg proposed is that an ordinary, first-in-first-out queue is inefficient because it is not a market. I disagree to some extent. Let's re-examine the act of arranging early arrivals. By arriving early, you sacrifice the liberty of arranging the day's tasks liberally, often risking postponing a couple of other chores to the next day and/or losing opportunities for spending the morning somewhere else. This *cost of flexibility and opportunity* is a bid[^1] for guarantee/priority of service. Yes, it's still not a market where you trade spots in the queue, but its auction-like nature makes it a much closer implementation than Landsburg's queue.
[^1]: Well, it's technically a payment, since you don't get your money back should you lose the auction (i.e., decide to bail out from the queue). However, since it's not a game of chance, I can't call it a gamble either.